# Sound waves calculations

yetar
Hello
I am interested in calculating the sound waves created by objects in air.
What is the resolution of details that needs to be dealt with in orer to calculate this?
Can it be calculated by using traits of the object such as mass density, geometry and other related attributes? Or do you need to deal in the level of particles and behaviour of small particles such as atoms?
Where there is reference material on this subject? books etc?

I would appreaciate your help on this matter.
Thanks in advance.

## Answers and Replies

Homework Helper
Gold Member
Well, what do you mean by calculating sound waves. There are many attributes of waves that can be calculated given the information you have. For instance teh wavelength of the fundamental sound wave made by a string is equal to 2 times the length of the string. The velocity of a wave is equal to its frequency times its wavelength. Is this the kinda stuff your looking for?

yetar
G01 said:
Well, what do you mean by calculating sound waves. There are many attributes of waves that can be calculated given the information you have. For instance teh wavelength of the fundamental sound wave made by a string is equal to 2 times the length of the string. The velocity of a wave is equal to its frequency times its wavelength. Is this the kinda stuff your looking for?
I want to calculate the values of the sum of sound waves in a certain point in space, created by some object.
If we take the string example, I want to know what is the value of the sound waves in a certain point outside the string. So I want to know the waves in the air and not the wave in the string itself.
How does a soundwave moves in the air? Does it change the density of the air?
By knowing what is the density over time in a certain point, I can know what will be the sound that a humen ear will hear in that point?
Do you know where I can find material on this problem?

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Homework Helper
Gold Member
Well, I can tell you that sound does move through air by changing the density of the air it moves through. More dense areas of air, denser than normal, would correspond to crests in a sine wave and ares of density less than that of normal air correspond to troughs. Other than that, I have no idea how to calculate the density at a certain point in a wave. If you take the string example, the wavelength and frequency of the wave in air is the same as that in the string, but other than that... This doesn't mean it can't be done. But if your looking to find the volume of a sound you hear, that corresponds to the amplitude of the wave. If your looking for the note played, that corresponds to the frequency of the wave I think, but other than that I have no idea.

yetar
What is the rigid bodies movement that create sound?
When a metal bell is being sound, what happens to that bell that cause it to create sound?
Does it vibrate? The whole body vibrate? or does the shape of the body changes in these vibrations like the string or a spring?

Homework Helper
Gold Member
Yes, the whole bell vibrates. Put you hand on a bell that's ringing and you can feel the vibration until the friction from your hand eventually brings the vibration to a stop, which brings the sound waves to a stop. When the rigid body vibrates, it vibrates the air around it which vibrates the air around that air and so on, spreading the vibration. That vibration through the air is the sound wave.

yetar
How do you calculate this vibration?
All I know about impact is the momentum (velocity*mass) is preserved.
However, I don't know what cause vibration?
How does an impact cause vibrations?
What are the laws related to that?

kishtik
G01 said:
For instance teh wavelength of the fundamental sound wave made by a string is equal to 2 times the length of the string.

Can you explain (or link to) why?

Homework Helper
Gold Member
kishtik said:
Can you explain (or link to) why?

Well, one wave length is the distance from a point on one wave to the same point on the next wave (or vibration) So if you start out at point that's right before a crest starts, then you'll end on a point that's right before the next crest, and that is one wavelength. So, in one wavelength you have one crest and one trough. Now think about when you pluck a string, like plucking a guitar string. You pull the string upward in the middle while both ends are tied down. This makes what looks like a wave crest, and when you let go it moves as far down as it can before being pulled back by its tied down ends, making what looks like a wave trough. Those are the crests and troughs of the sound wave vibrating in that string. One crest is equal to the legth of the string. One truough is equal to the length of the string. Put the wave and the trough together and you get a wavelength. so the wavelength would be equal to sum of the lengths of the crest and the trough. So,

on string length + one string length = 2 string lengths or 2X the length of the string. Lol I hoped I helped there.

Homework Helper
Gold Member
yetar said:
How do you calculate this vibration?
All I know about impact is the momentum (velocity*mass) is preserved.
However, I don't know what cause vibration?
How does an impact cause vibrations?
What are the laws related to that?

This vibration is the sound wave. If you want to know the frequency of the vibration, that is the frequency of the sound wave, etc. When some part of something is hit, like the part of the bell that was struck, it tries to move away from the rest of the bell because a force was applied to it, but the electrons of the atoms on the moving part are attracted to the protons on the rest of the bell and vice versa, so this electrical attraction pulles the moving part back, and the moving part pulls the rest of the bell a little bit and the whole bell starts shaking back and forth, thus causing a vibration. If the force used to hit the bell is more than this electrical force holding the bell together, then the moving part will break off of the other part and the bell will break. (Amazing how much went on in the liberty bell when it cracked huh? )

Anyway yetar, I still don't know what you mean by calculating the sum of sound waves in a certain point. What are you actually trying to find? As far as I know that'll do nothing but tell you how many sound waves there are at that point. I don't see how that could be useful. Maybe if you try to explain what property of sound you want to measure I can help a little better?

yetar
Thanks for the replies.
I will explain myself better.
Lets say we have a bell and a microphone, I hit the bell and then the microphone records the sound it creates.
The microphone "gives" me a one dimensional wave (amplitude over time).
Now I have the data of the shape and position of the bell, the position of the microphone and the data about the hitting of the bell.
Now I want to calculate what would the microphone record.
Is that possible?
A more specific question, is this calculation possible using only Newton's mechanics? or do I need to look into atoms and quantom physics?

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Science Advisor
yetar said:
Now I want to calculate what would the microphone record.
Is that possible?
Calculate what? Sound pressure level? dB levels? What exactly do you mean by calculate?

Mentor
yetar said:
Thanks for the replies.
I will explain myself better.
Lets say we have a bell and a microphone, I hit the bell and then the microphone records the sound it creates.
The microphone "gives" me a one dimensional wave (amplitude over time).
Now I have the data of the shape and position of the bell, the position of the microphone and the data about the hitting of the bell.
Now I want to calculate what would the microphone record.
Is that possible?
A more specific question, is this calculation possible using only Newton's mechanics? or do I need to look into atoms and quantom physics?
Your initial question made little sense, this makes better sense. Let's start even simpler, though: with a tuning fork. A tuning fork is a metal fork-shaped object. When struck, it vibrates at a frequency that depends on its mechanical properties: its dimensions and the elasticity of the metal it is made of. The tuning fork directly displaces air near it, turning its vibration into sound waves in the air (caveat - I think tuning forks use interference, but that's not important for this discussion).

If you are looking for the shape of the wave associated with a specific tuning fork, you're looking for natural frequency or resonant frequency. http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l4b.html [Broken] is some information. The amplitude depends on how hard it is struck.

Put even simpler, a spring-mass system is the most straightforward type of system to calculate natural frequency: its just sqrt(k/m), explained in more detail HERE. Vibration calculations quickly get far more complicated than that, though.

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kishtik
G01 said:
Lol I hoped I helped there.

Thank you.

yetar
russ_watters said:
Your initial question made little sense, this makes better sense. Let's start even simpler, though: with a tuning fork. A tuning fork is a metal fork-shaped object. When struck, it vibrates at a frequency that depends on its mechanical properties: its dimensions and the elasticity of the metal it is made of. The tuning fork directly displaces air near it, turning its vibration into sound waves in the air (caveat - I think tuning forks use interference, but that's not important for this discussion).

If you are looking for the shape of the wave associated with a specific tuning fork, you're looking for natural frequency or resonant frequency. http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l4b.html [Broken] is some information. The amplitude depends on how hard it is struck.

Put even simpler, a spring-mass system is the most straightforward type of system to calculate natural frequency: its just sqrt(k/m), explained in more detail HERE. Vibration calculations quickly get far more complicated than that, though.

Ok, thanks.
About vibration calculation, it is possible to calculate it with Newton's mechanics and without looking into atoms?
Just like you don't need to look into the atoms of a spring to calculate harmonic moition?
Are there any basic laws related to vibrations? What if I do want to calculate vibrations? where can I find reference on that?

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yetar
FredGarvin said:
Calculate what? Sound pressure level? dB levels? What exactly do you mean by calculate?
I want to calculate whatever I can then translate into the digital data that a computer microphon would record. The digital data recorded is just the shape of a one dimensional wave with no physical attribute related to it.

yetar
So, do you know how can I calculate these rigid bodies vibrations?