Question

A band is moving towards a fixed reflecting wall with speed $5$ m/s and emitting a sound of frequency $100$ Hz. A person is following the band with speed $20$ m/s detects the beats of frequency _______[take velocity of sound in air $=300$ m/s & in still water $=1500$ m/s]

• A. $3$ Hz
• B. $4$ Hz
• C. $3.55$ Hz
• D. $4.55$ Hz

Answer 1

The correct option is C $3.55$ Hz

Doppler's effect : $f_{observed}$ = $f_{source}$($\frac{\upsilon \pm {\upsilon }_o}{\upsilon \pm {\upsilon }_s}$)

Beat frequency = |$f_1$ - $f_2$ |

Frequency of sound emitted from the band heard directly by the observer = 100($\frac{300+20}{300+5}$)

=100($\frac{320}{305}$)

Frequency of sound reflected from the wall = frequency of sound received by it

=100( $\frac{300}{295}$)

Frequency of sound emitted from the band heard by the observer after reflection from the wall=100($\frac{300}{300-5}$)($\frac{300+20}{300}$)

=100( $\frac{320}{295}$ ) Beat frequency = |$f_1$ - $f_2$ |

=100*320($\frac{1}{295}$ - $\frac{1}{305}$)

= 3.55 Hz.