Question

A stationary source sends sound waves of the single wavelength. A wall approaches it with a velocity of $33\text{cm/sec}.$ The speed of sound waves in the medium is $330\text{m/sec},$ reflection of the waves on the wall brings about a change in wavelength by

• A. $0.1\%$
• B. $0.2\%$
• C. $0.3\%$
• D. $0.4\%$

Answer 1

Answer: (B)

$0.2\%$

Let wavelength of sound at source be ${\lambda }_1$.

So frequency is ${\nu }_1=v/{\lambda }_1$

where, $v=330m/s$ is the speed of sound in the medium.

The waves get reflected by moving wall so in this case observer is moving with velocity $v_o=33cm/s=0.33m/s$,

After reflection the wall acts like moving source with same velocity but opposite sign $v_s=-33cm/s=-0.33m/s$

So by Doppler effect, the frequency observed by wall is:

${\nu }_2={\nu }_1(v+v_o)/(v+v_s)={\nu }_1(330+0.33)/(330-0.33)=1.002{\nu }_1$

So, new wavelength, ${\lambda }_2=v/{\nu }_2=v/1.002{\nu }_1=0.998{\lambda }_1$

So change in wavelength is $=({\lambda }_1-{\lambda }_2)\times 100\%/{\lambda }_1=0.002\times 100=0.2\%$