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Question

A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by y=A0 sin(kxωt) then which of the following options represents a possible pressure wave through this medium?

A
ΔPosin(kxωt)
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B
ΔPocos(kxωt)
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C
ΔPocos(kxωt)
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D
ΔPocos(kx+ωt)
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Solution

The correct option is B ΔPocos(kxωt)
We know that relation between pressure wave and displacement wave is given by,
P=Bδyδx where P is the pressure, B is the bulk modulus of the medium and y is displacement of the particle.
Given,
y=A0 sin(kxωt)
Now, δyδx=A0k cos(kxωt)
So, P=Bδyδx=BA0k cos(kxωt)
P=ΔPocos(kxωt)

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