What is the phase difference between the disp | vedclass

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(B) In a sound wave,the displacement $y(x, t)$ is given by $y = A \sin(kx - \omega t)$.The pressure variation $\Delta P$ is related to the displacemen

Vedclass · Accepted Answer

$\frac{\pi}{2}$

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(B) In a sound wave,the displacement $y(x, t)$ is given by $y = A \sin(kx - \omega t)$.The pressure variation $\Delta P$ is related to the displacement by the relation $\Delta P = -B \frac{\partial y}{\partial x}$,where $B$ is the bulk modulus.Calculating the derivative: $\frac{\partial y}{\partial x} = Ak \cos(kx - \omega t)$.Thus,$\Delta P = -BAk \cos(kx - \omega t) = BAk \sin(kx - \omega t - \frac{\pi}{2})$.Comparing the phase of the displacement wave $(kx - \omega t)$ and the pressure wave $(kx - \omega t - \frac{\pi}{2})$,the phase difference is $\frac{\pi}{2}$.

What is the phase difference between the displacement wave and the pressure wave in a sound wave?

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