The speed of sound travels at a constant, depending on the medium it travels through. As amplitude increases or decreases frequency increases or decreases inversely to maintain this relation. I am somewhat confused, however, as to if this speed refers to the propagation of the sound wave as a longitudinal wave as well as the speed of the phonons (if I am correct in this thought) that move along the wave function as oscillating particles in the air. So my question is: do phonons vary in speed based on the frequency of the acoustic wave?
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Why do you say, "As amplitude increases or decreases frequency increases or decreases inversely to maintain this relation"? What relation? The speed is constant and depends neither on frequency nor on amplitude (within normal limits). – safesphere Sep 18 '17 at 01:11
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Yes, the group velocity ("speed") of phonons is frequency dependent. The group velocity is the gradient of the dispersion relation. Take a look at the phonon dispersion relation for any material, and you can see that the derivative of the curves is not constant, so the group velocity is not constant.
For long wavelength phonons (wavevector close to zero), the dispersion relation is nearly linear, so the magnitude of the gradient is nearly constant. Hence the group velocity is nearly constant. The group velocity in the limit of zero wavevector is "the speed of sound", and it leads to the frequency/wavelength relationships you are familiar with.
(Side note, when you write "amplitude", I think that you really mean "wavelength". There is no relation between the amplitude and the frequency, but there is a relation between the wavelength and frequency.)
lnmaurer
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