Amplitudes of longitudinal sound waves

[TP9109]

I'm coming back to physics after a long so apologies if this has a basic answer- How can the amplitude of a longitudinal sound wave be increased without increasing its wavelength? I understand what it would look like graphically if a low amplitude sine wave and high amplitude sine wave were representing this scenario (ie the two waves would have the same wavelength but their peaks and troughs would be displaced by different amounts from the equilibrium position showing the differences in amplitude like in graph below)

But how does that work in reality? When I imagine a longitudinal wave with higher amplitude I imagine it causing "more compression" of the particles of the medium and "more rarefaction" of the particles. Looking at just compression, wouldn't the particles have to "stray further" from their original rest position in order to move closer and collide more with the next particles in the line to achieve this higher compression (and thus higher pressure). Straying further from the original position though means a longer wavelength since a greater distance is traveled during the cycle of the wave. So the only other way I can think of the amplitude increasing whilst keeping a constant wavelength is if we make the wave carry more energy whilst stopping the particles from "straying further" from rest position? Is this energy in the form of heat maybe? Quite confused by this and have tried looking online for answers so any insight into this is appreciated!

 

[Dale]

Straying further from the original position though means a longer wavelength since a greater distance is traveled during the cycle of the wave.

Straying further from the equilibrium position does not imply a longer wavelength. At any moment there are many peaks at different distances from the source. The wavelength is determined by the distance between two successive peak displacements. The size of the displacement itself doesn’t matter.

Of course, if the displacements are large enough you will get dispersive and other nonlinear waves instead of nice linear ones, but that is a different topic.

 

[davenn]

Straying further from the original position though means a longer wavelength since a greater distance is traveled during the cycle of the wave.

no, that's incorrect and your diagram demonstrates that. the distance between any peak ( or trough)
is the same for the low amplitude as it is for the high amplitude.

Just as playing a single note on any musical instrument ... play a middle "c" it can be played loudly or softly
It's amplitude has changed, it's frequency, aka wavelength, hasn't

Dave

 

[TP9109]

Thanks for your reply, that makes more sense now

 

[TP9109]

Just as playing a single note on any musical instrument ... play a middle "c" it can be played loudly or softly
It's amplitude has changed, it's frequency, aka wavelength, hasn't

Thanks for your reply, that makes more sense. So if we say that this animation represents that soft middle "c" note being played:

https://www.acs.psu.edu/drussell/Demos/waves/Lwave-Red-2.gif

I understand that the animation for the loud middle c would keep same frequency and wavelength but just its amplitude would change, but I'm struggling to visualise how that higher amplitude would appear in the animation? A higher amplitude would mean each compression "strip" area in the animation would contain more particles therefore more pressure- does that mean the "thickness" of the strips would be increased as more particles are involved in the compression? Or I guess another way is if strip thickness stays the same but with the particles having more energy than soft c? Thanks again

 

[A.T.]

does that mean the "thickness" of the strips would be increased

They don't have a specific "thickness", the pressure has a gradient, and for a louder sound the pressure difference and so the pressure gradient are steeper.

 

[berkeman]

Thanks for your reply, that makes more sense. So if we say that this animation represents that soft middle "c" note being played:

https://www.acs.psu.edu/drussell/Demos/waves/Lwave-Red-2.gif

Wow, what a cool animation! The professor who put it together looks to be pretty fascinating:

https://www.acs.psu.edu/drussell/

 

[Dale]

I'm struggling to visualise how that higher amplitude would appear in the animation?

The peaks would be more concentrated for a higher amplitude wave.

Low amplitude:

High amplitude:

 

[sophiecentaur]

Thanks for your reply, that makes more sense now

For a medium like air (or steel or water) the amount the particles are displaced is proportional to the force on them, This is the basis of simple harmonic motion. The best proof for you that amplitude doesn't affect frequency of oscillation is to look at the way a pendulum behaves.

You could do this yourself, easily. Make up a pendulum with a light string and an object with some reasonable mass (a fishing weight or a chunky steel nut). Measure the time for ten cycles of swing with a small displacement (say +/-5 degrees) and then for a larger displacement (+/-10 degrees) for those values you should find very little difference in the times - showing that the frequency doesn't change) This works despite the fact that a simple pendulum motion is not pure SHM.