For the pressure variation in a longitudinal wave represented as P=Pocos(ωt−kx), the density (ρ) equation for the given medium is best represented by
(ρo is the density of the medium at pressure Po)
A
ρ=ρosin(ωt−kx)
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B
ρ=−ρosin(ωt−kx)
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C
ρ=ρocos(ωt−kx)
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D
ρ=−ρocos(ωt−kx)
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Solution
The correct option is Cρ=ρocos(ωt−kx) We know that if pressure is high in a particular region of a medium then density is also high and if pressure is low then density is also low.
This means pressure and density are in phase. ⇒Δϕ=0
So, for pressure equation P=Pocos(ωt−kx), density equation will be ρ=ρocos(ωt−kx).