Sound WavesHardBloom L3

Question

A sound waves is travelling towards right and its S-t graph is as shown for x = 0.

What will be density vs x graph at t = T/4

Options

A.
B.
C.
D.

Solution

Sol. S = S0 sin (ωt + Kx)

∆ P = B S0K cos (ωt – Kx)

As PM = ρRT

So ρ = ρ0 cos (ωt – Kx)

⇒ ρ = $\rho_{0}\cos\left( \omega \times \frac{T}{r} - Kx \right)$ (at t = $\frac{T}{4}$)

⇒ ρ = $\rho_{0}\cos\left( \frac{\pi}{2} - Kx \right)$ = ρ0sin Kx

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