Question

In sound wave, $V_w$ is the wave velocity and $V_p$ is particle velocity. Then:

• A. ${\overrightarrow{V}}_w||{\overrightarrow{V}}_p$
• B. ${\overrightarrow{V}}_w\perp {\overrightarrow{V}}_p$
• C. ${\overrightarrow{V}}_w\times {\overrightarrow{V}}_p=0$
• D. ${\overrightarrow{V}}_w.{\overrightarrow{V}}_p=0$

Answer 1

Answer: (A), (C)

${\overrightarrow{V}}_w\times {\overrightarrow{V}}_p=0$

Sound wave is a longitudinal wave in which direction of both particle velocity and wave velocity are parallel.

i.e ${\overrightarrow{V}}_w||{\overrightarrow{V}}_p$

${\overrightarrow{V}}_w\times {\overrightarrow{V}}_p=V_w{V}_p\sin 0^{\circ }=0$

and ${\overrightarrow{V}}_w.{\overrightarrow{V}}_p=V_p{V}_w\cos 0^{\circ }\ne 0$

Hence, option (a) and (c) are correct.