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I'm studying reverb from a first principles standpoint and I'm finding it difficult to find this answer in my studies.

Firstly is this statement correct?

"The quantity of sound waves ejected into a space is dictated by each individual sound source in a space and what pitches and how many pitches (e.g. chords) they are playing."

In other words, if i pluck an A string on a guitar with the A being 440hz, that means that single pluck has ejected 440 sound waves into the space which are now reflecting off surfaces?

Secondly, how do these waves travel in terms of direction? Is there any consistency to their path of travel or are they uncontrollable in their direction?

Thirdly, once a sound wave bounces off a wall, how does it travel in terms of direction?

Many thanks folks! This is regarding natural reverb.

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    I'm voting to close this question as off-topic because I think it will be better answered on the physics.SE, and hasn't a practical connection with a problem in music making. – Tim H Nov 28 '19 at 8:58
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    I'm voting to not close this question as it has a lot to do with music practice - not only for the musicians but also for all the "victims" of musical practice! (because music is often - as Wilhelm Busch says - connected with noise. – Albrecht Hügli Nov 28 '19 at 9:14
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    @Tim I find your position to be rather nonsensical. We are talking about reverberation.. you know, the ones used for classical music live performances in specially designed music venues? Music is physics ultimately so I guess none of it belongs here? And the practical connection is understanding reverb and how it works so I can manage it in my mix. What more of a connection to music making would one need. – Seery Nov 28 '19 at 13:09
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    Ofcourse, music is sound, and acoustics is very important to making music. But I think your question is just about the physics of sound in general. I think your question would be more on topic if you could describe why you need to know what you want to know. What do you want to do? How do you imagine to use the information this answers will give in your music-making? As it is now it's like asking about the nature and the physics of photons on a site on the visual arts. But maybe I'm alone with this opinion? – Tim H Nov 28 '19 at 13:26
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    To conclude: I honestly believe you will get much better answers on this specific question on the physics.SE. – Tim H Nov 28 '19 at 13:33
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1) The quantity of sound waves produced in air depends on the intensity or amplitude. If you pull your guitar string back a very short distance from its normal resting position, then the oscillations in air particles will be small, and they won't bang against your ear drum as hard. This produces a quieter-sounding noise.

The frequency 440 Hz is how many complete wave cycles you produce per second. So every second, your string is vibrating back and forth 440 times. After the initial pluck, though, the intensity & amplitude start to die off, and eventually, causing the produced waves to become smaller and smaller with time until the string ceases to produce any more waves.

2) Sound waves are spherical, which means they travel outwards in all dimensions. Sound is nothing more than compressions in the air molecules/density, followed by rarefactions/expansions in the air. When your guitar string pushes against the surrounding air, this generates a 3D sphere of compression that travels out in all directions, essentially expanding evenly in all directions as it spreads through the room.

3) Once a wave bounces off a wall, each individual ray follows the law of reflect (angle of incidence = angle of reflection).

Reflected wavefronts can be easily mapped using ray tracing, i.e., the reflected ray leaves at an angle to the surface equal to the angle of incidence ("law of reflection").

https://ccrma.stanford.edu/~jos/pasp/Reflection_Spherical_Plane_Waves.html

Here's an example of what this looks like.

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    Check out reuk.github.io/wayverb which is a software reverb simulator that uses ray tracing. – Brian THOMAS Nov 28 '19 at 17:14
  • Great answer! So to summarize, a spherical wave will eject firstly in a linear motion from a sound source and the size of that wave will depend on the level of amplitude from the sound source. If a string vibrates 440 times per second along with its additional harmonics, there are 440+ sound waves being ejected into the room per second. Correct? – Seery Nov 28 '19 at 22:21
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    @Seery, sounds like you've got the right idea! Also, check out this answer where I talk some about the physical origins of sound. Regarding spherical waves and linear motion: if a sound is produced in the middle of the room, then the rays will travel out in all directions. Each ray travels in a straight line until it reaches a boundary, and then it reflects. But the rays are sent out in all directions. – jdjazz Nov 29 '19 at 2:22
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    @BrianTHOMAS that is SO COOL!!!! I can't wait to use that--thanks so much for sharing!! – jdjazz Nov 29 '19 at 2:22
  • @jdjazz thanks again! – Seery Nov 29 '19 at 2:32
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I refer you to Wikipedia.

The motion of sound can be hard to understand because we can't see its propagation. We can sometimes understand it more easily by analogy to waves we can see, for example waves on the surface of water, or light waves from a light bulb. Although they are different kinds of waves (sound waves are longitudinal whereas water and light waves are transverse), their behaviour is more similar than different. Here's a quick demo to understand the difference between longitudinal and transverse waves.

If i pluck an A string on a guitar with the A being 440hz, that means that single pluck has ejected 440 sound waves into the space which are now reflecting off surfaces?

Essentially, yes, but the guitar string is not simply vibrating at 440Hz. It's also vibrating at 880, 1320, etc -- harmonics. All of these frequencies are going out into the room. They don't travel in isolation. They're all interfering with each other to create a single complicated waveform. Yes, the sound will reflect off of surfaces in your room.

How do these waves travel in terms of direction? Is there any consistency to their path of travel or are they uncontrollable in their direction?

Under idealized conditions, sound travels outwards in all directions equally. The wavefront is an expanding sphere created by each 'quanta' of sound traveling in a straight line away from the source.1 By analogy, think of how light travels outwards from a lightbulb. As the the sphere grows, the sound's kinetic energy is being spread thinner and thinner, which is why sound intensity dissipates over distance in accordance with the inverse-square law.

In the case of both sound and light, obstacles encountered by the wave will impede or alter its course. Waves can reflect, refract, and diffract, which is to say they can bounce off of and/or bend around obstacles. Assuming the sound is made up of many frequencies, like a musical tone, the different frequencies may respond to these obstacles differently.

Once a sound wave bounces off a wall, how does it travel in terms of direction?

The sound will reflect off of the surface such that the reflected angle is equal to the incident angle -- eg: if sound traveling northeast strikes a wall running east-west, the reflected sound will be traveling southeast. To continue the light analogy, if your sound source is a light bulb, then each hard surface in your room is a mirror. Soft surfaces can absorb sound, ie not reflect it. Higher frequencies are absorbed more easily. On the other hand, very low frequencies can actually travel right through walls almost as if they weren't there. Low frequencies are very difficult to control.

There is a phenomenon called standing waves. This is when the size of a chamber (such as a room) is the same as the wavelength of a sound (or a multiple of it), resulting in the wave just hanging out there seemingly unchanged overtime. Because its wavelength matches the size of the space, it appears stationary, hence the name. For a visual aid, you can setup standing waves in a sink of water.

1 In actuality, each collision between air molecules is like a new tiny sound source creating a new tiny expanding sphere. But if you average out all the billions of these tiny spheres, you get the one big sphere I'm describing.

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    Music must be hard to understand as well, because we can't see it? – piiperi Reinstate Monica Nov 28 '19 at 10:38
  • Great answer. But don't many surfaces give diffuse/scattered reflections, i.e. at many angles not the same as the incident angle? In any case, I think there should be a TLDR: It's complicated :-) – gidds Nov 28 '19 at 14:56
  • @gidds Yes an uneven surface will scatter sound. An uneven surface is just lots of little surfaces, each of which will reflect the sound such that the angle of incidence and reflection are still the same. A TLDR would be a good idea. I'll edit. – ibonyun Nov 28 '19 at 17:35
  • @ibonyun another great answer! " Higher frequencies are absorbed more easily. On the other hand, very low frequencies can actually travel right through walls almost as if they weren't there. Low frequencies are very difficult to control." does this indicate why it isn't favorable to add reverb to bass and kicks? Thank you for your response. – Seery Nov 28 '19 at 22:28
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    @Seery I think the reason you don't usually put reverb on bass is because it can quickly get muddy, especially if there are other low frequency instruments competing for space in the mix. You totally can add reverb to kicks and bass, but you'll probably want to high-pass the reverb so that it doesn't contain (much) low frequency information. You can get the desired sense of space just from mids. It is not uncommon to put reverb on kick drums, and drum buses often add reverb too. I don't think any of this has much to do with bass frequencies being able to pass through walls. – ibonyun Nov 29 '19 at 5:31
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In other words, if i pluck an A string on a guitar with the A being 440hz, that means that single pluck has ejected 440 sound waves into the space which are now reflecting off surfaces?

No. The string will start generating sound waves at a rate of 440/second. How many waves it will generate, depends on how long you allow the string to vibrate. If you don't dampen the string, it will vibrate for a few seconds, generating waves that get weaker and weaker until they disappear under the threshold of our hearing.

If you allow the string to vibrate for exactly 1 second, you will generate 440 waves.

Actually it's a bit more complicated than that. A guitar also generates harmonics: frequencies that are a multiple of the 440 Hz ground tone.

  • Thank you for clarifying this Hobbes, much appreciated! – Seery Nov 28 '19 at 22:29

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