physics

Q: If the solid does not expand significantly , the wavelength of sound does not change at all . Why ?

The speed of sound in a solid depends on the elasticity of the soild and its density. The lower the desnity, the higher will be the sound speed.

Expansion of a solid leads an increase in volume but the mass of which remains unchanged, thus the density of the solid decreases. As a result, the speed of sound in the solid increases.

Since speed of sound = frequency x wavelength, any decrease of speed is indicated by a shortening of wavelength.

It is therefore obvious that if the solid doesn't expand significantly, the speed of sound through it has not changed and the wavelength should remain as before.
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Q: If wavelength remains unchanged ,then Δf / f = Δ c / c Why ?
can you prove ?

Since c = f.w, where w denotes the wavelength
Δ c = w.Δ f, since w remains unchanged

thus, Δ c/c = (w.Δ f)/w.f = Δ f/f

According to the wave equation,

c = fw

where w = wavelength

if w = constant

change in c = change in f

So Δ c / c = Δf / f