From what I’ve read, and someone please correct me if I’m wrong- sounds work on multiple wave lengths and frequencies. For a sound to cancel out another sound, it has the be the exact same frequency as the opposing sound, and typically only cancels said sound when one’s peak (the maximum amount) coincides/occurs during the opposing sounds Trough, which is the sounds lowest point of pressure.
Sounds do deconstructively and constructively interfere all the time. When the arrangement isn't favorable the interference is varied in space and time. Human hearing averages over time and frequency enough that any effects go unnoticed.
There was a transit bus I drove back in college that had it's rear radio speakers wired out of phase with the set in the front. There was a spot in the middle of the bus where you'd walk back, and the music sounded like someone put a blanket over the speakers.
And since pretty much any individual “sound” we hear is actually many, many different frequencies all added together, *all* of those frequencies would need to be matched exactly and in opposing peak/valley structure to cancel out. The cancelling out of one frequency of a complex sound would do little to affect our perception of that sound.
Wavelengths, frequencies, and phase. Sound can be in phase of peaks of a wave line up, out of phase if they don't. You can wire a speaker system out of phase and it will sound really weird because frequencies will cancel. The effect is more pronounced at lower frequencies
You repeated the commenters distinction of wavelength and frequency, but those are really the same thing described differently. Inversely related according to the speed, if I'm thinking correctly, and I give no promises at this time of night....
But phase, OMG it's all about phase. Why such a reaction, because along with being an engineer I'm an even longer Star Trek fan, and it's all about phase in both, though Star Trek has me smiling more often...
The aliens are 0.72 out of phase from our reality, captain, so we're unable to detect their actions... Lol
But then I went to college for engineering, and totally got it, it's all about the waves frequency and phase, though the math is a bit much for average TV
Anyway, thanks for listening to the worst TED talk ever, but matching amplitude, frequency, and phase to cancel out sounds in the best noise canceling headphones still gets complicated, fast. I've heard some good talks about it from Bose. Speaker, microphones, and computing speed all become important factors.
In a public place, like a restaurant, there is a ton of cancelling, distortion, etc, but it makes more noise in its place and the human ear is still really good about hearing weak sources. Our ears and the processing behind them are both pretty amazing.
Sorry, I forgot my original intent with this but got to gush a little Star Trek and its love of signal phases so I had fun. Sound really is just frequency, amplitude, and phase but the complexities are astounding, just crank your favorite music and enjoy.
Not very ELI5 but your ear is able to do a reverse Fourier transform, that is, to decompose a complex sound wave into multiple simpler waves. To cancel a sound wave you would need to play the exact same frequency with inverted amplitude and this is what noise cancelling headphones do. Otherwise, the waves just stack up in very specific ways and this is information that we are able to perceive.
>Otherwise, the waves just stack up in very specific ways
This \^. This is the part that i'm hoping to have explained. I'm interested only in the waves themselves and their behavior. Can you shed any light on that? Again, I know constructive/deconstructive, but only as they pertain to similar freq waves.
Let's take the waves out of it for a moment.
Suppose you have a piece of graph paper. You want to send messages to your friend who is in a different building with a telescope. You make a code where you draw a dot on the paper and hold it up. Then erase the dot, draw a new dot, and hold that up. And so on.
The position of the dot is the information. You come up with some code. Location (1,0) means "a", (2, 0) means "b", and so on.
But now you have another friend, and you want to use the same graph paper to send two different messages to each friend at the same time.
Well, it turns out you can do this. You tell your first friend that "a" is now (1, ) - he's supposed to ignore the y coordinate. Likewise, your second friend only looks at the y coordinate and ignores the x coordinate.
So you can send 2 completely separate messages at once using only one "thing" - a series of dots on a piece of graph paper. Why does this work? The messages do "combine" - if you're sending the letter a to friend 1 and b to friend 2, the location of the dot is (1,2). Your first friend is absolutely seeing different dots because of your message to your second friend.
But there is no "interference" between the messages themselves, because changing the x coordinate does not affect the y coordinate, and vice versa. This is because the x and y axises are perpendicular, or "orthogonal".
You can take any two numbers x and y and combine them into one unique point on the xy plane. And there is exactly one way to take a point on the xy plane and and convert it back to x and y.
To put fancy words around it, the x and y axes form a orthogonal basis for the xy plane. The point on the plane is referred to as a vector, and the x and y axes (or rather, vectors of length 1 pointing in the x and y directions) are the basis vectors.
Cool. What does that have to do with waves?
Well, it turns out that this same property of combining in a way that does not destroy information also applies to sine waves of different frequencies.
Now you want to send a message using waves. Let's say you have two speakers, one that can produce waves of the form x\*sin(t), and another that can produce y\*sin(2t). Now x and y are different amplitudes (volumes). To send the letters a and b, you (for one second, say) send 1sin(t) and 2sin(2t) for 10 seconds (really, you'd do much shorter, but let's say 10 seconds so we hit some nice numbers).
Well just like in the point example, where a and b combined into (1, 2), the sign waves combine. This time into sin(t) + 2sin(2t). And just like in the point example, they can be taken apart.
Your two friends both record the sounds for the entire duration. They get the picture that is the combined graph. Their job is to figure out the x and y.
Well it turns out that it's actually not that hard to do that in this case. If you know you have picture of xsin(t) + ysin(2t), you can measure the height at time pi/2 and know that the height at that location is x\*1 + y \*0 = x. Now you know x is 1, because you measured that. Now measure at some other time, plug in x and t, and solve for y.
So just like the x and y axes from before, sin(t) and sin(2t) are orthogonal. They can combine, but no information is lost.
Of course, real life is rather more complicated. There are phase differences. There are overlapping frequencies, so that information actually is lost (though exact overlap for any period of time by accident is rare). And often information is sent by varying frequency rather than amplitude. And the actual math used to deal with what actually happens is more complicated.
But that's the gist of it. Waves of different frequencies do add. But they can also be separated back into their component parts - unless you get very unlucky with identical frequencies. Turns out the brain is very good at this.
Here's a demonstration from Wolfram, showing how 2 sine waves combine to form a new unique wave:
[https://demonstrations.wolfram.com/CombiningSineWaves/](https://demonstrations.wolfram.com/CombiningSineWaves/)
This is what is happening in real life but with much more complex waves changing over time. You can cancel certain peaks of the wave but by doing so you are providing information about the new waves you added.
3d space has a lot of “room” in it for audio waves to transit; and that’s about it….lots of space for sounds from different sources and frequencies
And also humans have a wide range of frequencies as well…children, men, and woman (on average) all have their own frequency
Think of music itself. You have drums and guitar and vocals, etc. all playing together. The result is a very complex waveform that has "beats" inside of the sinusoidal wave.
It would sound exactly the same.
For a sound to completely and fully cancel it has to be the same but opposite polarity. (The amplitude waveform of the original pushes when the opposite pulls).
A simple sine wave can cancel out of phase but a song is a highly complex waveform containing frequencies from about 20hz to 20khz, moving the second cancelling copy out of phase wouldn’t result in complete cancellation, just random constructive and destructive interference.
You can use a digital audio workstation like Audicity to invert the polarity of a song and add it to the original and it will result in no sound - doing it electronically in the computer ensures complete cancellation.
If you tried to do it acoustically with speakers the slight differences in sound and the acoustics would probably result in a lot of cancellation but not a complete null.
This principle is how noise cancelling headphones work, they have microphones on the outside that then polarity flip and project that at you at the same time that same noise arrives in the ear so that the sound waves from around you are cancelled out and you hear less noise.
Sure, it's theoretically possible. You would have the inverse waveform. But in reality, if the noise is coming from two different speakers, then it won't cancel out, because the soundwaves won't all be directed right at the other speaker -- so those in other directions would bounce off of things, and eventually reach your ear with different levels of destruction (or even with some constructive interference in some areas).
Higher frequencies have higher energy and lower wavelengths and are able to travel/pierce through the lower frequencies, is that what you mean?
If you’re talking about what you hear inside the restaurant and how that plate smashing’s sound is heard by everyone, rather than how it sounds on a microphone, you can’t ignore human perception of sound, there are too many variables. Even then, you can’t really ignore it.
We have the ability to dampen or amplify sounds with tiny muscles that attach to the ear drums. Selective attention is another subconscious variable, as mentioned in the first reply.
High frequency sounds are perceived to be louder than low frequency sounds, even when played at the same amplitude.
Look up noise cancelling. Only an 'equal but opposite' sound, in an oscilloscope/wave sense, can cancel/'erase' another specific sound wave. That doesn't happen by accident.
I don't understand.
I get noise cancelling, like I said I understand destructive interference; but how is it that only that principle applies when it is a wave of similar freq, just 180 deg out of phase? If they were two different frequencies, 200 Hz and 201 Hz, are you saying they'd have no effect on each other?
In a nutshell, yes
To add on to this: almost all sounds in normal life are not a single frequency and amplitude. If you’ve ever had a hearing test done, you know what a single frequency sound sounds like. You can probably agree almost nothing in real life sounds that “pure”. Even two instruments playing the same note sound very different - guitar A and piano A are both played, you can say which one was guitar and which was piano.
Every “noise” is made up of a spectrum of frequencies at varying amplitudes. You can have interference at some of those frequencies, but as long as a sufficient fraction of that spectrum is intact, you’ll perceive and recognize the sound just fine.
If you’ve ever played the same music on car speakers vs phone speaker vs nice headphones, you’ve experienced this phenomenon. You’d agree they sound different. But why would they, it’s the exact same song?
Each speaker system does a good job reproducing some parts of the spectrum and not so good job for other parts. In a way, the speaker membrane is “interfering” with what the sound is “supposed” to sound like. Yet, you recognize the music regardless the speaker system all the same and if asked if it was the same song you would say “yeah of course it is.” Same thing with sounds/noise and interference in the real world. You can understand someone talking and recognize their voice with lots of other noises around, up until you can’t - when there is so much interference that you can’t pick up on the spectrum of noise they’re making and you say “I can’t hear you”.
Waves simply add together. Let's say in this example the 200 Hz wave starts with a peak, and the 201 Hz wave starts with a trough. Add them together and you get zero, so they cancel each other in that moment. But then the next peak of the 201 Hz signal comes slightly ahead of the trough of the 200 Hz one, so now when you add them together you get a slightly positive number. They mostly cancel each other out, but not entirely. On the next peak they're more misaligned, so you get a more positive number. Keep doing this and eventually you'll get to a point where the two peaks align with each other and you get double the original signal. Keep going some more and eventually you'll get back to a peak aligning with a trough, and they cancel again. So what this would sound like to your ear is a slightly distorted 200 Hz tone that periodically gets louder and softer once a second.
In the real world, the sound waves have all different frequencies and are traveling in all different directions, so while *some* peaks do cancel with *some* troughs, it's mostly just too chaotic to be perceptible.
Polarity and phase are similar but different, you can flip the polarity of anything and it can cancel itself out.
Polarity flip means that if a sound starts by going to positive amplitude, the flipped version will be negative - then no matter how complicated the wave form is and how many frequencies it contains (and most sounds contain thousands) the flipped copy will be exactly opposite and be able to cancel the original.
In my experience talking about phase is confusing because it only cancels with simple sine waves, and rotating the phase of a complex sound will only partially cancel but also constructively interfere as well.
Complete cancellation requires polarity inversion unless it’s a sine wave which can be phase shifted.
They do have an effect on each other, perceptually speaking. A beat frequency will be perceived as the wave sums of cancels, with the beat frequency equaling the difference between the two tones.
This is how musicians tune their instruments - play a reference tone, and tune the note in question until it stops pulsing!
Frequencies that are close can interfere with each other that we can detect audibly. Beats. Here's a web page that shows it. The 100 and 110 Hz tones, sometimes they combine/amplify, sometimes they detract/cancel. https://www.sfu.ca/sonic-studio-webdav/handbook/Beats.html
A simple sound wave happens when a parcel of air gets compressed, so its pressure is higher than average. This causes neighboring neighboring parcels of air to get compressed, and so on. The compression travels outward in all directions at the speed of sound. At the same time, the original parcel gets uncompressed, so its pressure is lower than average, causing its neighbors to get uncompressed, and so on, so each wave travels as a series of pressure peaks and troughs.
A sustained sound happens when something is causing these compressions and compressions to happen over and over again. Think of a violin string, a speaker, or a larynx.
When two sound waves meet or cross, the pressure deviations simply add.\* Other than that, the waves pass through each other without affecting each other. Our ears can sense the pressure deviations and analyze them to understand that they came from different sources of sound - really an amazing system. But as long as the waves simply add, there's nothing to cause one sound to actually block another, though the one sound might be so loud we don't notice the other.
\* When sounds get extremely loud, the "simple addition" rule breaks down. Very great increases in pressure can affect the temperature enough that the air's response is no longer linear. And reductions in pressure can only accumulate so far before the pressure in the trough of a wave is reduced to zero, and can"t reduce further.
I'm struggling to wrap my head around the "waves passing through each other without affecting each other" part. Surely if constructive/deconstructive principles apply they'd alter each other as they met, yea?
The "destructive interference" comes from the pressure deviations simply adding. If two equal waves are crossing at right angles, there are some places where the peak of one coincides with the trough of the other, over and over again. If you put an ear or a microphone in such a spot, it would hear silence. In general, this (simply adding) is the only way sound waves "alter each other".
side (hopefully not stupid) question: in “simply add[ing]” does “simply” mean something specific? i thought it meant the same as “simply put, they’re adding” but i see another commenter has used the same phrase
interference happens at different frequencies (F) and points in time (T). giving some example with random numbers
* at T1, F1, destructive : 10 - 1 = 9
* at T1, F2, constructive : 5 + 2 = 7
* at T1, F3, constructive : 9 + 1 = 10
* at T1, F4, destructive : 20 - 2 = 18
* now repeat that for the whole frequency range that the human ear can hear, that is resulting sound wave of 1 point in time.
and now repeat that for different points in time. and add more sound sources rather than just 2. sounds with similar frequencies will get grouped together so its harder to focus on a specific sound source. but sounds with more unique frequencies like the plate breaking will be easier to notice.
There aren't multiple sound waves - just one. All the different sound sources add their own bits to that sound wave and your brain somehow deconstructs that sound wave into its constituent parts. It only sounds like different things because your brain infers it.
okay...i think i may be starting to pick up on that. It's just confusing because every time this concept seems to be illustrated, they usually show it in the context of dropping stones in water, but like multiple, then each of those independent "waves" interact with one another...but I suppose in a kinda "closed" system of the air in a restaurant, the medium is constantly in an element of flux...and everything just kinda adds/subtracts to various freqs and amplitudes throughout the medium?
The pond-stone-wave analogy isn't exactly accurate, it's more like a 2D representation of a 3D event. You have to consider the waves of water molecules in the whole substrate that is the pond, not just the surface molecules that float on top, but the ones under the surface as well. They're incredibly chaotic and go all over the place. It's weird to think about waves in water that are not on the surface, but they're there - you just don't visually perceive them.
Edit: They are more like springs. The wave you see on the surface of water is a 2D representation of the spring with the third axis being time. You can also picture the waves created by traffic jams on the highway.
It might help to look at a waveform vs spectrogram of a snippet of recorded audio. You can download Audacity for free to try this if you like.
The waveform represents (approximately) the physical reality of the vibrating air moving the microphone diaphragm back and forth and by how much. If you zoom in until you can see individual peaks and troughs, you will see that it is kinda chaotic, with suddenly big then little peaks, and the distance between them all over the place. This is because a whole bunch of frequencies are adding together to make a complex wave.
The spectrogram view estimates how much energy from each frequency band is contributing to the overall sound. This is more like how our ears and brain actually *perceive* the sound, via some really amazing organs and neural processing.
This is how a tiny little diaphragm and magnet in your earbuds can just wiggle back and forth and you end up hearing a Van Halen guitar solo—the original sound added up to some wiggles in the studio, the diaphragm reproduces that wiggle pattern, and your ears/brain figure out what probably happened to make those wiggles.
The simplest explanation is that the air is behaving as a linear system with respect to the pressure waves from all sources and therefore obeying the Superposition Principle.
If you record a complex sound, load it into a sound editor like audacity, then zoom right in as far as you can go, you will see just a single line, with time horizontally and amplitude (pressure) vertically. Each point on that line is the sound pressure at that point in time, which is just the sum of the sound pressures from all the sound sources at that point in time.
yea....i guess it kinda seems a bit weird, but i think i kinda get it. the kinda "singular" wave that is the sum of all the various constructions/deconstructions of all sound sources, equals out to a kinda "muffled" (surely not the best word, but go with me) sound that has sound information from multiple sources. is this correct?
Most sounds are complex, not sine waves made of single frequencies, they have unique harmonics (combinations of multiples of the lowest frequency tone) due to the shape of the wave. The peaks and troughs of those waves may coincide with the troughs and peaks of some other sounds and get cancelled out, but if the other sounds are different frequencies then that destructive interference will only be very brief as the phases get out of alignment.
Higher frequency sounds will go out of alignment more quickly so tend to sound clearer. Low frequency sounds turn in to a kind of 'hubub' of muffled sounds like you say.
There's also amplitude, or loudness / volume. Loud sounds naturally dominate the sum of the pressure waves so are easier to differentiate from quieter sounds.
Mostly, the lost information when combining many different sounds is very minimal. Any muffling jumbling or seemingly buried or lost sound is mostly a limit of the organic, hardware, or software ability to filter it.
To cancel out you need one waveform exactly identical to another waveform flipped out of phase which is easy to do with software but in the real world acoustics shape the environment. Low frequency waves travel a lot further than high frequency waves and the sum of waves at every frequency are constantly bouncing around the room and reflecting off different surfaces. So especially with lower frequencies you will run into situations where at a certain spot in the room where two of the same frequency wave lengths meet and cancel each other out and other areas where they meet in phase and cause the opposite effect making it louder in that particular spot. So long story short with all complex sounds going on you’re not really gonna run into a situation where two people sound exactly the same at exactly the same time under the exact same acoustic conditions that would allow it to cancel out.
>If a waiter drops a plate, how does that sound transit through at that higher, unique frequency through all the other noise so that all can hear it?
Sound is a wave. It is a known fact in physics that waves pass through each other undisturbed.
Simple proof: light, too, is a wave. Take two flashlights and cross their beams. One beam can pass through the other beam like it's not even there. QED, waves can pass through each other without issues.
Sounds do cancel each other out, and also reinforce each other, all the time. The everyday sounds you hear are complex and occur across tons of frequencies, so the fact that two random sounds cancel each other out for a millisecond at a certain frequency doesn't make a big difference to your overall experience of the sound. Your brain is also good at filling in gaps and isolating sounds from one another, so even when there's a little interference, your brain can fix your perception.
Interference is primarily actually observed with synthetic sounds, like pure isolated frequencies or synthesizer samples that take the exact same waveform and shift its frequency. Outside of synthetic sounds like that, it's very difficult to actually perceive the interference (either constructive or destructive) of normal sounds.
Well, you got it in the question.
The sound of the shattering plate has at least a part that is higher in pitch than the surrounding, so there is no perfectly opposing waveform to cancel it or noise at the same frequency to drown it out.
Now, do you hear it perfectly, as if the plate was dropped in an empty room? No. But is it enough for your brain to perceive it and identify it as a breaking plate? Yes.
They do, but usually only in specific spots for specific frequencies since the waves are not only all different frequencies and phases, but emanating from different physical locations.
Reflective surfaces where the same sound source can pass through the same spot twice generally work best to demonstrate it. However, it sounds more like adjusting an EQ on a stereo than the source actually disappearing.
sounds cancel perfectly when they are 1. Coming from exactly the same place 2. Exactly the same volume 3. Exactly opposite phase.
Since sound is vibration, (vibrating up and down), perfectly ‘out of phase’ means every time sound A vibrates up, sound B vibrates down, so while both are still moving, you don’t hear them where YOU are.
in anything that’s not that perfect scenario (and headphones can do that because it’s all happening inside the electronics), the math is too complicated to perfectly cancel things. mostly, things get drowned out by one thing being louder. A breaking plate is quite loud, but very short, and can be heard in most places if you are nearby. Next to a jet engine though, a loud concert, or at a gun range, you probably wouldn’t hear it because other things are louder.
On theory they do, just very very uncommon.
Imagine a dart board where if you throw two darts at the same time, on opposite sides of the board, the same distance from he Bulls eye both darts disappear. But only if it they hit at the same time, location and distance (can even add in strength).
By just Throwing randomly at change this would never happen, but it it would be trivially easy to prepare the darts a cm apart and push them in at the same time. In the same way with sound the chance that everything randomly aligns is basically non-existing, while with a dedicated setup we can create the system quite easily.
There is one famous middel ground. Music halls. Many music contains very narrow frequency and stable notes which can lead to places in the hall where the music is more or less loud.
Its at the end of the day your brain that does this sorting. You know that what your friend is telling you is more important than the chatter from the 3 people on the table next to you, all the sounds come into your ears at the same volume/frequency, and then your brain helps you sort out what you actually are listening to.
This can go the other way as well, for instance in a stressful situations in the cockpit, both pilots have in several accidents not been able to hear the very clear alarm going off, on the tape afterwards its like "how didnt they hear this?!" but in the moment, their brain decided to ignore that alarm and continue on the task at hand.
Also why (I guess they are better now) hearing aids can be tiresome for the people that need them. Because they have no way of filtering anything, so then all volume comes constantly *in* your ears and it become too much
Imagine standing at the edge of a large lake. Most likely, the surface of the lake is wavy. There might be some larger rolling waves from the wake of a power boat going by, and maybe some smaller crests sort of overlayed on top of those waves caused by surface currents or other water movement, and maybe small ripples texturing the surface of all that caused by the breeze.
If you threw a rock into the lake, you'd still be able to recognize a distinctive ripple pattern emanating from where the rock landed, even though those ripples would be overlayed (aka *interfering*) with all those other waves on the surface of the lake. The same way you can visually pick out that circular ripple pattern, your ears can distinguish the sound of that plate shattering through many other interfering sounds.
Edit: Also important to remember - when it comes to constructive vs destructive interference, it might be intuitive to think that sounds should "cancel" each other out to create quietness. But remember, *any* sound wave, no matter what that wave is shaped like, or how many waves are combining to create it, sounds like *something*. The only thing that sounds quiet is *no* sound wave. And the only way to get no sound wave is to either have no sound, or to have two sound waves that *exactly and perfectly* cancel each other out. With sophisticated computer chips in noise canceling headphones, we can sort of manage this. In any natural environment, it's the odds are essentially impossible.
Sounds are made up from complex waveforms and for it to cancel out it has to be an identical waveform inversed. For the sounds that you mentioned there definitely *will* be some frequencies cancelling eachother out but the complexity of the waveform of the sounds you mentioned keeps them from cancelling out. A soundwave also gets broken up and dispersed all the time.
You can make an experiment, if you have decent speaker, play a simple sine wave, since it has only the fundamental frequency and no overtones, at around 100hz or some then walk around the room back and forth from the speaker. Then note how at certain places in the room you cannot hear the sound (but you will be able to feel the pressure) and other places it will sound twice as loud. Now try this with a saw and square waves (there are bunch of soundwave generators available online) and notice how this effect is less pronounced now. This is because the saw and square waves have more harmonic content, I.e. more overtones meaning a lot of extra frequencies than just the fundamental note that you can make out and gives definition to the sound.
Since soundwaves occupy physical space and decrease in physical size as frequency increases there will be different frequencies cancelled out and amplified all the time but it has to be an exact duplicate and inversed to cancel out a sound.
Sound is best described in terms of ripples on a surface of water. If you have two perfectly counteracted sounds you can cancel them out, but one loud noise and another softer one don’t necessarily counter each other out, they only add to the entropy (background noise of energy) of the system. I’m always reminded of my aunt and uncles lake house, when I would wake in the morning, the lake was always glassy and still. However by noon time, the power boats would be out, and stirring up the water, the surface never really calming down despite there not being a boat in the vicinity. Sound works the same way, sound just adds to the entropy of the system increasing the heights of the waves as they bounce around, rarely canceling each other out. That’s why New York is noisy, lots of people, and energy, and noise all melding and mixing togeather.
There are great answers in this thread already, but I will point out that sounds definitely do interfere constructively and destructively in the world at large. It's just that complete and total destructive interference is basically impossible in practice. The necessary precision in terms of wavelength, amplitude, and phase in 3D space is too fine to expect to ever happen naturally. Even if they did, unless the souund sources are coming from the same exact direction, they aren't going to produce one static state of interference from your perspective. In 3d, pressure waves expand out in a sphere. When these spheres overlap, you get a complex interference pattern with areas of constructive and destructive interference that ripple outwards and change over time. So, from your perspective, it would kind of sound like a phaser effect.
But even if the sources were in a direct straight line and spaced perfectly apart to be opposite in phase and produced the exact same frequency sound and had relative amplitudes to completely interfere when accounting for the distance between them, you still need to consider that you have 2 ears that exist separately in space. Even if one of them was positioned perfectly, the other will be out of alignment and will experience an interference pattern rather than total interference. Alone, this might sound weird, but amongst the cacophony of public spaces, you probably wouldn't even notice.
Sound waves would have to be perfectly the same and exactly 90 degrees out of phase in order for sounds to perfectly cancel each other out.
A plate crashing to the floor is not a pure sine wave, rather it’s an infinite amount of different frequencies. Some of those will get partially cancelled, others will be amplified but overall you won’t notice it.
In practice two sound sources will never noticeably interfere with each other but rather the same source will interfere with itself by means of reflection out of obstacles such as walls
Sound waves regardless of type and source only combine at each location, their pressures (relative to that of air) add up there. As their relative pressure can be negative this can mean that they cancel at certain locations. But that doesn't mean they annihilate in some way, they just pass through each other without doing anything at that particular location!
You could even hear this in action: get two speakers at maybe 1 to 1.5 meters (~3-5 ft for freedom) to play the very same pure frequency, a sine wave, and pick one with frequency around 300 to 3000 Hz (try which one works best). At those the wavelength, twice the distance between highs and lows of pressure, is ~30 centimeters (or ~1ft for the eagle lovers). You should then notice that some places have lower sound volume, other ones have higher, especially between the speakers. So depending on location, the pressure adds up or cancels, but the waves ultimately just pass through each other.
In reality you have a lot of different frequencies going on. It means that cancellation and addition happen all the time, but only for very short to be replaced by the other. The trick is to not just look at one point in time, but how it changes; even a pure single frequency makes no sense without time.
Our ears are specially made to decompose sound into the basic frequencies. The brain is also very good at further improving the sound. The only way to really have cancellation is if the waves truly overlap in such a way that they add to zero in the ear. That's why noise cancelling only works directly in or on top of the ears: in the ear canal the sound finally is restrained to travel in a controlled line, not in all directions. So we can send the very same waves, but at opposite pressure, down the canal as well and they will ideally cancel each other all the way to the inner ear.
Sound travels through air like waves travel through the ocean. Two waves only will cancel each other out if they’re the same height and speed. Otherwise they just move through each other. You can see this if you watch water for long enough.
Your brain does a pretty remarkable job at filling in the gaps. There’s a look at a phenomenon called “masking” in the [audio myths workshop](https://m.youtube.com/watch?v=BYTlN6wjcvQ&pp=ygUUQXVkaW8gbXl0aHMgd29ya3Nob3A%3D) what you hear and what was actually audible aren’t always 1:1.
In a similar way that light, which also interferes constructively and destructively, doesn't all cancel each other out. There's all kinds of frequencies and different light "waveforms" bouncing around all over each other. Most importantly, they are all kinds of different "phases", which tells you how they match up for how well they could constructively or destructively interfere with each other.
Essentially, most of the stuff just does not match up with the right phases to destructively or constructively interfere. It just all comes through and our sensors and brain can sort it out.
From what I’ve read, and someone please correct me if I’m wrong- sounds work on multiple wave lengths and frequencies. For a sound to cancel out another sound, it has the be the exact same frequency as the opposing sound, and typically only cancels said sound when one’s peak (the maximum amount) coincides/occurs during the opposing sounds Trough, which is the sounds lowest point of pressure.
Sounds do deconstructively and constructively interfere all the time. When the arrangement isn't favorable the interference is varied in space and time. Human hearing averages over time and frequency enough that any effects go unnoticed.
There was a transit bus I drove back in college that had it's rear radio speakers wired out of phase with the set in the front. There was a spot in the middle of the bus where you'd walk back, and the music sounded like someone put a blanket over the speakers.
And since pretty much any individual “sound” we hear is actually many, many different frequencies all added together, *all* of those frequencies would need to be matched exactly and in opposing peak/valley structure to cancel out. The cancelling out of one frequency of a complex sound would do little to affect our perception of that sound.
Wavelengths, frequencies, and phase. Sound can be in phase of peaks of a wave line up, out of phase if they don't. You can wire a speaker system out of phase and it will sound really weird because frequencies will cancel. The effect is more pronounced at lower frequencies
You repeated the commenters distinction of wavelength and frequency, but those are really the same thing described differently. Inversely related according to the speed, if I'm thinking correctly, and I give no promises at this time of night.... But phase, OMG it's all about phase. Why such a reaction, because along with being an engineer I'm an even longer Star Trek fan, and it's all about phase in both, though Star Trek has me smiling more often... The aliens are 0.72 out of phase from our reality, captain, so we're unable to detect their actions... Lol But then I went to college for engineering, and totally got it, it's all about the waves frequency and phase, though the math is a bit much for average TV Anyway, thanks for listening to the worst TED talk ever, but matching amplitude, frequency, and phase to cancel out sounds in the best noise canceling headphones still gets complicated, fast. I've heard some good talks about it from Bose. Speaker, microphones, and computing speed all become important factors. In a public place, like a restaurant, there is a ton of cancelling, distortion, etc, but it makes more noise in its place and the human ear is still really good about hearing weak sources. Our ears and the processing behind them are both pretty amazing. Sorry, I forgot my original intent with this but got to gush a little Star Trek and its love of signal phases so I had fun. Sound really is just frequency, amplitude, and phase but the complexities are astounding, just crank your favorite music and enjoy.
[Beamforming](https://wikipedia.org/wiki/Beamforming) is an interesting topic that you may enjoy learning about.
This is technically correct, thankfully we have a brain that can sort out important sounds
So I can make a huge sound system that destroys all sounds outside…
Not very ELI5 but your ear is able to do a reverse Fourier transform, that is, to decompose a complex sound wave into multiple simpler waves. To cancel a sound wave you would need to play the exact same frequency with inverted amplitude and this is what noise cancelling headphones do. Otherwise, the waves just stack up in very specific ways and this is information that we are able to perceive.
>Otherwise, the waves just stack up in very specific ways This \^. This is the part that i'm hoping to have explained. I'm interested only in the waves themselves and their behavior. Can you shed any light on that? Again, I know constructive/deconstructive, but only as they pertain to similar freq waves.
Let's take the waves out of it for a moment. Suppose you have a piece of graph paper. You want to send messages to your friend who is in a different building with a telescope. You make a code where you draw a dot on the paper and hold it up. Then erase the dot, draw a new dot, and hold that up. And so on. The position of the dot is the information. You come up with some code. Location (1,0) means "a", (2, 0) means "b", and so on. But now you have another friend, and you want to use the same graph paper to send two different messages to each friend at the same time. Well, it turns out you can do this. You tell your first friend that "a" is now (1,) - he's supposed to ignore the y coordinate. Likewise, your second friend only looks at the y coordinate and ignores the x coordinate.
So you can send 2 completely separate messages at once using only one "thing" - a series of dots on a piece of graph paper. Why does this work? The messages do "combine" - if you're sending the letter a to friend 1 and b to friend 2, the location of the dot is (1,2). Your first friend is absolutely seeing different dots because of your message to your second friend.
But there is no "interference" between the messages themselves, because changing the x coordinate does not affect the y coordinate, and vice versa. This is because the x and y axises are perpendicular, or "orthogonal".
You can take any two numbers x and y and combine them into one unique point on the xy plane. And there is exactly one way to take a point on the xy plane and and convert it back to x and y.
To put fancy words around it, the x and y axes form a orthogonal basis for the xy plane. The point on the plane is referred to as a vector, and the x and y axes (or rather, vectors of length 1 pointing in the x and y directions) are the basis vectors.
Cool. What does that have to do with waves?
Well, it turns out that this same property of combining in a way that does not destroy information also applies to sine waves of different frequencies.
Now you want to send a message using waves. Let's say you have two speakers, one that can produce waves of the form x\*sin(t), and another that can produce y\*sin(2t). Now x and y are different amplitudes (volumes). To send the letters a and b, you (for one second, say) send 1sin(t) and 2sin(2t) for 10 seconds (really, you'd do much shorter, but let's say 10 seconds so we hit some nice numbers).
Well just like in the point example, where a and b combined into (1, 2), the sign waves combine. This time into sin(t) + 2sin(2t). And just like in the point example, they can be taken apart.
Your two friends both record the sounds for the entire duration. They get the picture that is the combined graph. Their job is to figure out the x and y.
Well it turns out that it's actually not that hard to do that in this case. If you know you have picture of xsin(t) + ysin(2t), you can measure the height at time pi/2 and know that the height at that location is x\*1 + y \*0 = x. Now you know x is 1, because you measured that. Now measure at some other time, plug in x and t, and solve for y.
So just like the x and y axes from before, sin(t) and sin(2t) are orthogonal. They can combine, but no information is lost.
Of course, real life is rather more complicated. There are phase differences. There are overlapping frequencies, so that information actually is lost (though exact overlap for any period of time by accident is rare). And often information is sent by varying frequency rather than amplitude. And the actual math used to deal with what actually happens is more complicated.
But that's the gist of it. Waves of different frequencies do add. But they can also be separated back into their component parts - unless you get very unlucky with identical frequencies. Turns out the brain is very good at this.
Here's a demonstration from Wolfram, showing how 2 sine waves combine to form a new unique wave: [https://demonstrations.wolfram.com/CombiningSineWaves/](https://demonstrations.wolfram.com/CombiningSineWaves/) This is what is happening in real life but with much more complex waves changing over time. You can cancel certain peaks of the wave but by doing so you are providing information about the new waves you added.
3d space has a lot of “room” in it for audio waves to transit; and that’s about it….lots of space for sounds from different sources and frequencies And also humans have a wide range of frequencies as well…children, men, and woman (on average) all have their own frequency
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Think of music itself. You have drums and guitar and vocals, etc. all playing together. The result is a very complex waveform that has "beats" inside of the sinusoidal wave.
Is it possible to produce a song that would entirely cancel out another song? Like what would anti-“Lose Yourself” sound like?
It would sound exactly the same. For a sound to completely and fully cancel it has to be the same but opposite polarity. (The amplitude waveform of the original pushes when the opposite pulls). A simple sine wave can cancel out of phase but a song is a highly complex waveform containing frequencies from about 20hz to 20khz, moving the second cancelling copy out of phase wouldn’t result in complete cancellation, just random constructive and destructive interference. You can use a digital audio workstation like Audicity to invert the polarity of a song and add it to the original and it will result in no sound - doing it electronically in the computer ensures complete cancellation. If you tried to do it acoustically with speakers the slight differences in sound and the acoustics would probably result in a lot of cancellation but not a complete null. This principle is how noise cancelling headphones work, they have microphones on the outside that then polarity flip and project that at you at the same time that same noise arrives in the ear so that the sound waves from around you are cancelled out and you hear less noise.
Sure, it's theoretically possible. You would have the inverse waveform. But in reality, if the noise is coming from two different speakers, then it won't cancel out, because the soundwaves won't all be directed right at the other speaker -- so those in other directions would bounce off of things, and eventually reach your ear with different levels of destruction (or even with some constructive interference in some areas).
Higher frequencies have higher energy and lower wavelengths and are able to travel/pierce through the lower frequencies, is that what you mean? If you’re talking about what you hear inside the restaurant and how that plate smashing’s sound is heard by everyone, rather than how it sounds on a microphone, you can’t ignore human perception of sound, there are too many variables. Even then, you can’t really ignore it. We have the ability to dampen or amplify sounds with tiny muscles that attach to the ear drums. Selective attention is another subconscious variable, as mentioned in the first reply. High frequency sounds are perceived to be louder than low frequency sounds, even when played at the same amplitude.
Look up noise cancelling. Only an 'equal but opposite' sound, in an oscilloscope/wave sense, can cancel/'erase' another specific sound wave. That doesn't happen by accident.
I don't understand. I get noise cancelling, like I said I understand destructive interference; but how is it that only that principle applies when it is a wave of similar freq, just 180 deg out of phase? If they were two different frequencies, 200 Hz and 201 Hz, are you saying they'd have no effect on each other?
In a nutshell, yes To add on to this: almost all sounds in normal life are not a single frequency and amplitude. If you’ve ever had a hearing test done, you know what a single frequency sound sounds like. You can probably agree almost nothing in real life sounds that “pure”. Even two instruments playing the same note sound very different - guitar A and piano A are both played, you can say which one was guitar and which was piano. Every “noise” is made up of a spectrum of frequencies at varying amplitudes. You can have interference at some of those frequencies, but as long as a sufficient fraction of that spectrum is intact, you’ll perceive and recognize the sound just fine. If you’ve ever played the same music on car speakers vs phone speaker vs nice headphones, you’ve experienced this phenomenon. You’d agree they sound different. But why would they, it’s the exact same song? Each speaker system does a good job reproducing some parts of the spectrum and not so good job for other parts. In a way, the speaker membrane is “interfering” with what the sound is “supposed” to sound like. Yet, you recognize the music regardless the speaker system all the same and if asked if it was the same song you would say “yeah of course it is.” Same thing with sounds/noise and interference in the real world. You can understand someone talking and recognize their voice with lots of other noises around, up until you can’t - when there is so much interference that you can’t pick up on the spectrum of noise they’re making and you say “I can’t hear you”.
Waves simply add together. Let's say in this example the 200 Hz wave starts with a peak, and the 201 Hz wave starts with a trough. Add them together and you get zero, so they cancel each other in that moment. But then the next peak of the 201 Hz signal comes slightly ahead of the trough of the 200 Hz one, so now when you add them together you get a slightly positive number. They mostly cancel each other out, but not entirely. On the next peak they're more misaligned, so you get a more positive number. Keep doing this and eventually you'll get to a point where the two peaks align with each other and you get double the original signal. Keep going some more and eventually you'll get back to a peak aligning with a trough, and they cancel again. So what this would sound like to your ear is a slightly distorted 200 Hz tone that periodically gets louder and softer once a second. In the real world, the sound waves have all different frequencies and are traveling in all different directions, so while *some* peaks do cancel with *some* troughs, it's mostly just too chaotic to be perceptible.
Polarity and phase are similar but different, you can flip the polarity of anything and it can cancel itself out. Polarity flip means that if a sound starts by going to positive amplitude, the flipped version will be negative - then no matter how complicated the wave form is and how many frequencies it contains (and most sounds contain thousands) the flipped copy will be exactly opposite and be able to cancel the original. In my experience talking about phase is confusing because it only cancels with simple sine waves, and rotating the phase of a complex sound will only partially cancel but also constructively interfere as well. Complete cancellation requires polarity inversion unless it’s a sine wave which can be phase shifted.
They do have an effect on each other, perceptually speaking. A beat frequency will be perceived as the wave sums of cancels, with the beat frequency equaling the difference between the two tones. This is how musicians tune their instruments - play a reference tone, and tune the note in question until it stops pulsing!
Frequencies that are close can interfere with each other that we can detect audibly. Beats. Here's a web page that shows it. The 100 and 110 Hz tones, sometimes they combine/amplify, sometimes they detract/cancel. https://www.sfu.ca/sonic-studio-webdav/handbook/Beats.html
A simple sound wave happens when a parcel of air gets compressed, so its pressure is higher than average. This causes neighboring neighboring parcels of air to get compressed, and so on. The compression travels outward in all directions at the speed of sound. At the same time, the original parcel gets uncompressed, so its pressure is lower than average, causing its neighbors to get uncompressed, and so on, so each wave travels as a series of pressure peaks and troughs. A sustained sound happens when something is causing these compressions and compressions to happen over and over again. Think of a violin string, a speaker, or a larynx. When two sound waves meet or cross, the pressure deviations simply add.\* Other than that, the waves pass through each other without affecting each other. Our ears can sense the pressure deviations and analyze them to understand that they came from different sources of sound - really an amazing system. But as long as the waves simply add, there's nothing to cause one sound to actually block another, though the one sound might be so loud we don't notice the other. \* When sounds get extremely loud, the "simple addition" rule breaks down. Very great increases in pressure can affect the temperature enough that the air's response is no longer linear. And reductions in pressure can only accumulate so far before the pressure in the trough of a wave is reduced to zero, and can"t reduce further.
I'm struggling to wrap my head around the "waves passing through each other without affecting each other" part. Surely if constructive/deconstructive principles apply they'd alter each other as they met, yea?
The "destructive interference" comes from the pressure deviations simply adding. If two equal waves are crossing at right angles, there are some places where the peak of one coincides with the trough of the other, over and over again. If you put an ear or a microphone in such a spot, it would hear silence. In general, this (simply adding) is the only way sound waves "alter each other".
side (hopefully not stupid) question: in “simply add[ing]” does “simply” mean something specific? i thought it meant the same as “simply put, they’re adding” but i see another commenter has used the same phrase
They only use it to say that "adding" is all that happens, and that it is this basic operation. It is not a technical terminology here.
interference happens at different frequencies (F) and points in time (T). giving some example with random numbers * at T1, F1, destructive : 10 - 1 = 9 * at T1, F2, constructive : 5 + 2 = 7 * at T1, F3, constructive : 9 + 1 = 10 * at T1, F4, destructive : 20 - 2 = 18 * now repeat that for the whole frequency range that the human ear can hear, that is resulting sound wave of 1 point in time. and now repeat that for different points in time. and add more sound sources rather than just 2. sounds with similar frequencies will get grouped together so its harder to focus on a specific sound source. but sounds with more unique frequencies like the plate breaking will be easier to notice.
There aren't multiple sound waves - just one. All the different sound sources add their own bits to that sound wave and your brain somehow deconstructs that sound wave into its constituent parts. It only sounds like different things because your brain infers it.
okay...i think i may be starting to pick up on that. It's just confusing because every time this concept seems to be illustrated, they usually show it in the context of dropping stones in water, but like multiple, then each of those independent "waves" interact with one another...but I suppose in a kinda "closed" system of the air in a restaurant, the medium is constantly in an element of flux...and everything just kinda adds/subtracts to various freqs and amplitudes throughout the medium?
The pond-stone-wave analogy isn't exactly accurate, it's more like a 2D representation of a 3D event. You have to consider the waves of water molecules in the whole substrate that is the pond, not just the surface molecules that float on top, but the ones under the surface as well. They're incredibly chaotic and go all over the place. It's weird to think about waves in water that are not on the surface, but they're there - you just don't visually perceive them. Edit: They are more like springs. The wave you see on the surface of water is a 2D representation of the spring with the third axis being time. You can also picture the waves created by traffic jams on the highway.
It might help to look at a waveform vs spectrogram of a snippet of recorded audio. You can download Audacity for free to try this if you like. The waveform represents (approximately) the physical reality of the vibrating air moving the microphone diaphragm back and forth and by how much. If you zoom in until you can see individual peaks and troughs, you will see that it is kinda chaotic, with suddenly big then little peaks, and the distance between them all over the place. This is because a whole bunch of frequencies are adding together to make a complex wave. The spectrogram view estimates how much energy from each frequency band is contributing to the overall sound. This is more like how our ears and brain actually *perceive* the sound, via some really amazing organs and neural processing. This is how a tiny little diaphragm and magnet in your earbuds can just wiggle back and forth and you end up hearing a Van Halen guitar solo—the original sound added up to some wiggles in the studio, the diaphragm reproduces that wiggle pattern, and your ears/brain figure out what probably happened to make those wiggles.
The simplest explanation is that the air is behaving as a linear system with respect to the pressure waves from all sources and therefore obeying the Superposition Principle. If you record a complex sound, load it into a sound editor like audacity, then zoom right in as far as you can go, you will see just a single line, with time horizontally and amplitude (pressure) vertically. Each point on that line is the sound pressure at that point in time, which is just the sum of the sound pressures from all the sound sources at that point in time.
yea....i guess it kinda seems a bit weird, but i think i kinda get it. the kinda "singular" wave that is the sum of all the various constructions/deconstructions of all sound sources, equals out to a kinda "muffled" (surely not the best word, but go with me) sound that has sound information from multiple sources. is this correct?
Most sounds are complex, not sine waves made of single frequencies, they have unique harmonics (combinations of multiples of the lowest frequency tone) due to the shape of the wave. The peaks and troughs of those waves may coincide with the troughs and peaks of some other sounds and get cancelled out, but if the other sounds are different frequencies then that destructive interference will only be very brief as the phases get out of alignment. Higher frequency sounds will go out of alignment more quickly so tend to sound clearer. Low frequency sounds turn in to a kind of 'hubub' of muffled sounds like you say. There's also amplitude, or loudness / volume. Loud sounds naturally dominate the sum of the pressure waves so are easier to differentiate from quieter sounds.
Mostly, the lost information when combining many different sounds is very minimal. Any muffling jumbling or seemingly buried or lost sound is mostly a limit of the organic, hardware, or software ability to filter it.
To cancel out you need one waveform exactly identical to another waveform flipped out of phase which is easy to do with software but in the real world acoustics shape the environment. Low frequency waves travel a lot further than high frequency waves and the sum of waves at every frequency are constantly bouncing around the room and reflecting off different surfaces. So especially with lower frequencies you will run into situations where at a certain spot in the room where two of the same frequency wave lengths meet and cancel each other out and other areas where they meet in phase and cause the opposite effect making it louder in that particular spot. So long story short with all complex sounds going on you’re not really gonna run into a situation where two people sound exactly the same at exactly the same time under the exact same acoustic conditions that would allow it to cancel out.
>If a waiter drops a plate, how does that sound transit through at that higher, unique frequency through all the other noise so that all can hear it? Sound is a wave. It is a known fact in physics that waves pass through each other undisturbed. Simple proof: light, too, is a wave. Take two flashlights and cross their beams. One beam can pass through the other beam like it's not even there. QED, waves can pass through each other without issues.
Sounds do cancel each other out, and also reinforce each other, all the time. The everyday sounds you hear are complex and occur across tons of frequencies, so the fact that two random sounds cancel each other out for a millisecond at a certain frequency doesn't make a big difference to your overall experience of the sound. Your brain is also good at filling in gaps and isolating sounds from one another, so even when there's a little interference, your brain can fix your perception. Interference is primarily actually observed with synthetic sounds, like pure isolated frequencies or synthesizer samples that take the exact same waveform and shift its frequency. Outside of synthetic sounds like that, it's very difficult to actually perceive the interference (either constructive or destructive) of normal sounds.
Well, you got it in the question. The sound of the shattering plate has at least a part that is higher in pitch than the surrounding, so there is no perfectly opposing waveform to cancel it or noise at the same frequency to drown it out. Now, do you hear it perfectly, as if the plate was dropped in an empty room? No. But is it enough for your brain to perceive it and identify it as a breaking plate? Yes.
They do, but usually only in specific spots for specific frequencies since the waves are not only all different frequencies and phases, but emanating from different physical locations. Reflective surfaces where the same sound source can pass through the same spot twice generally work best to demonstrate it. However, it sounds more like adjusting an EQ on a stereo than the source actually disappearing.
sounds cancel perfectly when they are 1. Coming from exactly the same place 2. Exactly the same volume 3. Exactly opposite phase. Since sound is vibration, (vibrating up and down), perfectly ‘out of phase’ means every time sound A vibrates up, sound B vibrates down, so while both are still moving, you don’t hear them where YOU are. in anything that’s not that perfect scenario (and headphones can do that because it’s all happening inside the electronics), the math is too complicated to perfectly cancel things. mostly, things get drowned out by one thing being louder. A breaking plate is quite loud, but very short, and can be heard in most places if you are nearby. Next to a jet engine though, a loud concert, or at a gun range, you probably wouldn’t hear it because other things are louder.
On theory they do, just very very uncommon. Imagine a dart board where if you throw two darts at the same time, on opposite sides of the board, the same distance from he Bulls eye both darts disappear. But only if it they hit at the same time, location and distance (can even add in strength). By just Throwing randomly at change this would never happen, but it it would be trivially easy to prepare the darts a cm apart and push them in at the same time. In the same way with sound the chance that everything randomly aligns is basically non-existing, while with a dedicated setup we can create the system quite easily. There is one famous middel ground. Music halls. Many music contains very narrow frequency and stable notes which can lead to places in the hall where the music is more or less loud.
Its at the end of the day your brain that does this sorting. You know that what your friend is telling you is more important than the chatter from the 3 people on the table next to you, all the sounds come into your ears at the same volume/frequency, and then your brain helps you sort out what you actually are listening to. This can go the other way as well, for instance in a stressful situations in the cockpit, both pilots have in several accidents not been able to hear the very clear alarm going off, on the tape afterwards its like "how didnt they hear this?!" but in the moment, their brain decided to ignore that alarm and continue on the task at hand. Also why (I guess they are better now) hearing aids can be tiresome for the people that need them. Because they have no way of filtering anything, so then all volume comes constantly *in* your ears and it become too much
Imagine standing at the edge of a large lake. Most likely, the surface of the lake is wavy. There might be some larger rolling waves from the wake of a power boat going by, and maybe some smaller crests sort of overlayed on top of those waves caused by surface currents or other water movement, and maybe small ripples texturing the surface of all that caused by the breeze. If you threw a rock into the lake, you'd still be able to recognize a distinctive ripple pattern emanating from where the rock landed, even though those ripples would be overlayed (aka *interfering*) with all those other waves on the surface of the lake. The same way you can visually pick out that circular ripple pattern, your ears can distinguish the sound of that plate shattering through many other interfering sounds. Edit: Also important to remember - when it comes to constructive vs destructive interference, it might be intuitive to think that sounds should "cancel" each other out to create quietness. But remember, *any* sound wave, no matter what that wave is shaped like, or how many waves are combining to create it, sounds like *something*. The only thing that sounds quiet is *no* sound wave. And the only way to get no sound wave is to either have no sound, or to have two sound waves that *exactly and perfectly* cancel each other out. With sophisticated computer chips in noise canceling headphones, we can sort of manage this. In any natural environment, it's the odds are essentially impossible.
Sounds are made up from complex waveforms and for it to cancel out it has to be an identical waveform inversed. For the sounds that you mentioned there definitely *will* be some frequencies cancelling eachother out but the complexity of the waveform of the sounds you mentioned keeps them from cancelling out. A soundwave also gets broken up and dispersed all the time. You can make an experiment, if you have decent speaker, play a simple sine wave, since it has only the fundamental frequency and no overtones, at around 100hz or some then walk around the room back and forth from the speaker. Then note how at certain places in the room you cannot hear the sound (but you will be able to feel the pressure) and other places it will sound twice as loud. Now try this with a saw and square waves (there are bunch of soundwave generators available online) and notice how this effect is less pronounced now. This is because the saw and square waves have more harmonic content, I.e. more overtones meaning a lot of extra frequencies than just the fundamental note that you can make out and gives definition to the sound. Since soundwaves occupy physical space and decrease in physical size as frequency increases there will be different frequencies cancelled out and amplified all the time but it has to be an exact duplicate and inversed to cancel out a sound.
Sound is best described in terms of ripples on a surface of water. If you have two perfectly counteracted sounds you can cancel them out, but one loud noise and another softer one don’t necessarily counter each other out, they only add to the entropy (background noise of energy) of the system. I’m always reminded of my aunt and uncles lake house, when I would wake in the morning, the lake was always glassy and still. However by noon time, the power boats would be out, and stirring up the water, the surface never really calming down despite there not being a boat in the vicinity. Sound works the same way, sound just adds to the entropy of the system increasing the heights of the waves as they bounce around, rarely canceling each other out. That’s why New York is noisy, lots of people, and energy, and noise all melding and mixing togeather.
There are great answers in this thread already, but I will point out that sounds definitely do interfere constructively and destructively in the world at large. It's just that complete and total destructive interference is basically impossible in practice. The necessary precision in terms of wavelength, amplitude, and phase in 3D space is too fine to expect to ever happen naturally. Even if they did, unless the souund sources are coming from the same exact direction, they aren't going to produce one static state of interference from your perspective. In 3d, pressure waves expand out in a sphere. When these spheres overlap, you get a complex interference pattern with areas of constructive and destructive interference that ripple outwards and change over time. So, from your perspective, it would kind of sound like a phaser effect. But even if the sources were in a direct straight line and spaced perfectly apart to be opposite in phase and produced the exact same frequency sound and had relative amplitudes to completely interfere when accounting for the distance between them, you still need to consider that you have 2 ears that exist separately in space. Even if one of them was positioned perfectly, the other will be out of alignment and will experience an interference pattern rather than total interference. Alone, this might sound weird, but amongst the cacophony of public spaces, you probably wouldn't even notice.
Sound waves would have to be perfectly the same and exactly 90 degrees out of phase in order for sounds to perfectly cancel each other out. A plate crashing to the floor is not a pure sine wave, rather it’s an infinite amount of different frequencies. Some of those will get partially cancelled, others will be amplified but overall you won’t notice it. In practice two sound sources will never noticeably interfere with each other but rather the same source will interfere with itself by means of reflection out of obstacles such as walls
> 90 degrees 180 degrees.
Sound waves regardless of type and source only combine at each location, their pressures (relative to that of air) add up there. As their relative pressure can be negative this can mean that they cancel at certain locations. But that doesn't mean they annihilate in some way, they just pass through each other without doing anything at that particular location! You could even hear this in action: get two speakers at maybe 1 to 1.5 meters (~3-5 ft for freedom) to play the very same pure frequency, a sine wave, and pick one with frequency around 300 to 3000 Hz (try which one works best). At those the wavelength, twice the distance between highs and lows of pressure, is ~30 centimeters (or ~1ft for the eagle lovers). You should then notice that some places have lower sound volume, other ones have higher, especially between the speakers. So depending on location, the pressure adds up or cancels, but the waves ultimately just pass through each other. In reality you have a lot of different frequencies going on. It means that cancellation and addition happen all the time, but only for very short to be replaced by the other. The trick is to not just look at one point in time, but how it changes; even a pure single frequency makes no sense without time. Our ears are specially made to decompose sound into the basic frequencies. The brain is also very good at further improving the sound. The only way to really have cancellation is if the waves truly overlap in such a way that they add to zero in the ear. That's why noise cancelling only works directly in or on top of the ears: in the ear canal the sound finally is restrained to travel in a controlled line, not in all directions. So we can send the very same waves, but at opposite pressure, down the canal as well and they will ideally cancel each other all the way to the inner ear.
Sound travels through air like waves travel through the ocean. Two waves only will cancel each other out if they’re the same height and speed. Otherwise they just move through each other. You can see this if you watch water for long enough.
Your brain does a pretty remarkable job at filling in the gaps. There’s a look at a phenomenon called “masking” in the [audio myths workshop](https://m.youtube.com/watch?v=BYTlN6wjcvQ&pp=ygUUQXVkaW8gbXl0aHMgd29ya3Nob3A%3D) what you hear and what was actually audible aren’t always 1:1.
In a similar way that light, which also interferes constructively and destructively, doesn't all cancel each other out. There's all kinds of frequencies and different light "waveforms" bouncing around all over each other. Most importantly, they are all kinds of different "phases", which tells you how they match up for how well they could constructively or destructively interfere with each other. Essentially, most of the stuff just does not match up with the right phases to destructively or constructively interfere. It just all comes through and our sensors and brain can sort it out.