Lets say you have a plank is you hit it once and get t time if you hit is 2x as hard will it travel t/2? will it be the same or will it travel only slightly faster?
[Physics] Does the speed at which sound travel depend on the volume (amplitude) of the sound
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Best Answer
A plank is a complicated example to choose because it's a composite material with a complicated structure. A better choice would be a piece of iron or some other homogeneous material.
In that case the speed of sound is given by:
$$ v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}} $$
where $K$ is the bulk modulus and $G$ is the shear modulus. The bulk modulus is how easy the material is to compress, and the shear modulus is how easy it is to deform sideways. Under most circumstances these moduli are constants, so the speed of sound is a constant. So when you hit the metal twice as hard the speed of sound is unchanged. In other words the speed of sound is not affected by the intensity of the sound.
However the moduli are only approximately constant for relatively small deformations, and for large deformations their values will change. If you can make the sound so intense that the deformation of the metal enters the non-linear region then the moduli will change and therefore so will the speed of sound.
Another unrelated effect is that the compression caused by the sound will heat the metal, and the moduli generally decrease with temperature. So if the sound is so intense that it causes local heating the moduli will decrease and so will the speed of sound.
However I should emphasise that you need very high energies for the moduito change appreciably. Under most circumstances you can consider the speed of the sound to be constant and not affected by the volume.