Question

A sound wave of frequency $440Hz$ is passing through air. An $O_2$ molecule (mass $=5.3\times {10}^{-26}kg)$ is set in oscillation with an amplitude of ${10}^{-6}m$. Speed at the center of its oscillation is:

• A. $17.0\times {10}^{-5}m/s$
• B. $2.77\times {10}^{-5}m/s$
• C. $1.70\times {10}^{-5}m/s$
• D. $2.76\times {10}^{-3}m/s$

Answer 1

The correct option is D $2.76\times {10}^{-3}m/s$

Given, frequency of sound wave,

$f=440Hz$

Amplitude of oscillation, $A={10}^{-6}m$

Speed of the sound wave at the center of oscillation, $v_{\text{max}}=\omega A$

$v_{\text{max}}=2\pi fA$

$v_{\text{max}}=(2\times 3.14)\left(440\right)\left({10}^{-6}\right)$

$v_{\text{max}}=2.76\times {10}^{-3}m/s$

Final answer : (c)