Question

A sound wave propagates in a medium of Bulk's modulus $B$ by means of compressions and rarefactions. If $P_c$ and $P_r$ are the pressures at compression and rarefaction respectively, $a$ be the wave amplitude and $k$ be the angular wave number then,

• A. $P_c$ is maximum and $P_r$ is minimum
• B. $P_c$ is minimum and $P_r$ is maximum
• C. The pressure amplitude is Bak
• D. If the displacement wave is $y=a\sin (\omega t-kx)$, the pressure wave at any instant is represented as $P=P,\cos (\omega t-kx)$ which leads displacement wave by a phase angle of $\frac{\pi }{2}$

Answer 1

Answer: (A), (C), (D)

At points of compressure the pressure is more than that at rarefaction points hence option (A) is correct. The pressure amplitude in the medium in sound wave is given by the expression mentioned in option (C) hence it is correct and at any point the variation of preesure is ahead in phase compared to displacement variation by an angle $\pi /2$ hence option (D) is correct.