A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by y=−A0sin(kx−ωt) then which of the following options represents a possible pressure wave through this medium?
A
ΔPosin(kx−ωt)
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B
ΔPocos(kx−ωt)
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C
−ΔPocos(kx−ωt)
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D
−ΔPocos(kx+ωt)
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Solution
The correct option is BΔPocos(kx−ωt) 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=−A0sin(kx−ωt)
Now, δyδx=−A0kcos(kx−ωt)
So, P=−Bδyδx=BA0kcos(kx−ωt) ⇒P=ΔPocos(kx−ωt)