A sinusoidal sound wave is propagating in still air. At an instant of time displacement of a particle from its mean position is $\vec{y}$ , acceleration of the particle is $\vec{a}$ and velocity of propagation is $\vec{v}$ . Then

Moderate

A

$\vec{a}$ and $\vec{y}$ must be antiparallel whereas $\vec{v}$ and $\vec{a}$ may be parallel.
B

$\vec{y}$ and $\vec{v}$ may be parallel whereas $\vec{a}$ and $\vec{v}$ must be mutually perpendicular
C

$\vec{y}$ and $\vec{v}$ must be mutually perpendicular whereas $\vec{a}$ and $\vec{v}$ must be parallel.
D

$\vec{y}$ and $\vec{v}$ must be parallel whereas $\vec{a}$ and $\vec{v}$ are mutually perpendicular.

Solution

Sound wave is longitudinal wave. Each particle is executing simple harmonic motion about its mean position as shown in figure. Therefore $\vec{y}$ and $\vec{v}$ are oppositely directed, $\vec{a}$ and $\vec{v}$ must be parallel. Again when $\vec{y}$ and $\vec{v}$ are parallel, $\vec{a}$ and $\vec{v}$ must be antiparallel.

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