Why does particle displacement A increase sound pressure?

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Discussion Overview

The discussion revolves around the relationship between particle displacement and sound pressure, specifically addressing why an increase in maximum displacement (A) of molecules leads to an increase in sound pressure. Participants explore theoretical models, analogies, and mathematical relationships related to sound waves and molecular motion.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that increasing the maximum displacement A of the speaker correlates with an increase in sound pressure, as described by the equation pmax = BkA.
  • One participant questions the assumption that the displacement of the speaker equals the displacement of the molecules, suggesting that this may not apply to all molecules in the medium.
  • Another participant proposes that each molecule acts as a speaker for the next, which may justify the assumption of equal displacement.
  • There is a discussion about the harmonic oscillator model and its applicability to sound waves, with some participants noting that it simplifies calculations while providing results close to reality.
  • One participant speculates that the increase in sound pressure is due to the increase in the maximum speed of molecules as A increases, questioning whether this is the only reason for the observed effect.
  • Another participant emphasizes that the relationship between maximum displacement and sound pressure is fundamentally mathematical, asserting that Pmax depends on BkA and that all constants have equal weight in this relationship.
  • Concerns are raised about the implications of increased molecular speed and its relationship to temperature, with some participants expressing confusion over how this aligns with established properties of sound in air.

Areas of Agreement / Disagreement

Participants express differing views on the assumptions regarding molecular displacement and the implications of increased speed on sound pressure. There is no consensus on the reasons behind the relationship between displacement and sound pressure, and the discussion remains unresolved.

Contextual Notes

Participants highlight limitations in their understanding of the assumptions involved in the models discussed, particularly regarding the relationship between molecular speed, displacement, and temperature. The discussion also touches on the mathematical dependencies without reaching a definitive conclusion.

luckis11
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pressure=p(x,t)=BkAsin(kx-ωt)
http://www.physics.unomaha.edu/Sowell/phys2120/Lectures/Sound/Sound.pdf

Surely, when loudness-intensity-pressure increases, so does the maximum displacement A of the speaker.

Wrong thread title. My question is: Why increasing the maximum molecule displacement A increases sound pressure.

They also say that the A of the speaker is equal to the maximum displacement "A" of the molecule. Why that?
 
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luckis11 said:
They also say that the A of the speaker is equal to the maximum displacement "A" of the molecule. Why that?

Because the situation is analogous to a person pushing on a box. The displacement of the person is equal to the displacement of the box, isn't it?
 
That's not an answer. I can understand the assumption that it is so for the molecule that is "always in contact" with the speaker (assuming something per average etc as it moves before the speker starts moving). But why should this apply for all other molecules too?
 
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luckis11 said:
...But why should this apply for all other molecules too?

Because each molecule acts as a speaker for the next one?...

You could say that it is an assumption. The assumption then allows for a model that is sufficiently close to reality, where each molecule has an average position.

You may also want to read about the model for sound waves in solids which is closely related: http://en.wikipedia.org/wiki/Phonon
 
What about my first question: (assuming that the A of the speaker is equal to the A of each molecule):Why increasing the maximum molecule displacement A increases sound pressure?

Is it because when the A of the molecule increases then the maximum speed
umax=(√(k/m))A=ωΑ=2πfA and all other speeds also increase? And if indeed so, then that's the only reason?
 
luckis11 said:
What about my first question: (assuming that the A of the speaker is equal to the A of each molecule):Why increasing the maximum molecule displacement A increases sound pressure?

Is it because when the A of the molecule increases then the maximum speed
umax=(√(k/m))A=ωΑ=2πfA and all other speeds also increase? And if indeed so, then that's the only reason?

Ok, the basic model is this. Picture a row of molecules end to end. Each one has an average position that is fixed and it is allowed to oscillate left and right about that position. The displacement is called y (which may be - or +). The MAXIMUM displacement is A (when y = A or y = -A). This (+ a few other conditions) is called the harmonic oscillator model and it is used all throughout physics for all kinds of waves because it allows relatively simple calculations with sines and cosines and gives results that are often very close to reality. The assumption is thus a very classical and fundamental one. You get a lot of physics for relatively little math.

Now that slide on pressure. V is volume and S is the area of a plane parallel to the speaker. B is the bulk modulus of the medium (air). The math shown is then pretty straightforward. The end result pmax=BkA simply shows that if A increases, so must pmax, linearly. You just can't argue with that math.
 
I am not arguing with the math. I am asking what they are claiming. If you do not know the answer do not answer me that "there is an answer".

B is constant, so does k, right and the function of sin can only take values between 1 and -1, right? So the Pmax and (?) the Σ|p(t)|dt of a period or half a period, is dependent on A only. And I am asking why that. One answer is that the max speed of each molecule increases as A increases, and its average speed doubles when A doubles because the period T remains the same (see also the simulation http://www.ngsir.netfirms.com/englishhtm/Lwave.htm )
So its seems that the reason is the increase of speed of the molecules (note that all molecules in a wavefront are moving towards the same direction as the wavefront). So I am asking whether I concluded correctly and whether the increase of their speed is the only reason. And because I get such answers from physicists, now I changed my mind and I AM "arguing with the math". The doubling of the speed just because the A of the speker doubled a little, means that there is a considerable increase at temperature, which is false or at least it seems to contradict that "the speed of sound in air is 343 for room temperature no matter what the speaker does". So what's going on: What have I grasped wrong or what is wrong.
 
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luckis11 said:
I am not arguing with the math. I am asking what they are claiming. If you do not know the answer do not answer me that "there is an answer".

Not saying you are, I just didn't see what you wanted more.

luckis11 said:
B is constant, so does k, right and the function of sin can only take values between 1 and -1, right?

Yes.

luckis11 said:
So the Pmax and (?) the Σ|p(t)|dt of a period or half a period, is dependent on A only.

Pmax depends on BkA, it's the only I can say it, and all three constants have equal ponderation.

luckis11 said:
And I am asking why that.

I say it's because of the math. You're looking for something else.

luckis11 said:
One answer is that the max speed of each molecule increases as A increases, and its average speed doubles when A doubles because the period T remains the same (see also the simulation http://www.ngsir.netfirms.com/englishhtm/Lwave.htm ) So its seems that the reason is the increase of speed of the molecules (note that all molecules in a wavefront are moving towards the same direction as the wavefront). So I am asking whether I concluded correctly and whether the increase of their speed is the only reason.

The RMS speed of the molecules does increase, and that would increase the pressure, but I think that this is beyond the scope, and besides the point, of the talk.

luckis11 said:
And because I get such answers from physicists, now I changed my mind and I AM "arguing with the math".

This was unexpected. If you were offended, it was not my intention.

luckis11 said:
"The doubling of the speed just because the A of the speker doubled a little, means that there is a considerable increase at temperature, which is false or at least it seems to contradict that "the speed of sound in air is 343 for room temperature no matter what the speaker does". So what's going on: What have I grasped wrong or what is wrong.

Personnally, I would not take the temperature into account, because IMO, for each area of increased pressure, there is an area of decreased pressure as well, so that if you were to calculate T(x), the average temperature along x would be the same whether or not there was a wave.

I thank you sir for giving me the opportunity to review sound, and I hope I was at least a little helpful.
 
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Dr Lots-o'watts said:
Personnally, I would not take the temperature into account, because IMO, for each area of increased pressure, there is an area of decreased pressure as well, so that if you were to calculate T(x), the average temperature along x would be the same whether or not there was a wave.

Excuse me?
 
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