Question

Two sound sources $S_1$ and $S_2$ of frequencies 324 Hz and 320 Hz are placed at certain separation. An observer is moving away from $S_1$ towards $S_2$ on line joining them. If he hears no beats then speed of observer is $(v=344m/sec):$

• A. 20 m/s
• B. 10 m/s
• C. 5 m/s
• D. 2.1 m/s

Answer 1

Answer: (D)

2.1 m/s

Observer mowing away from $S_1$ :

Apparent frequency $f_1=f_o[\frac{v-v_o}{v}]$

So, $f_1=$ $324[\frac{344-v_o}{344}]$ ........(1)

Observer mowing towards $S_2$ :

Apparent frequency $f_2=f_o[\frac{v+v_o}{v}]$

So, $f_2=$ $320[\frac{344+v_o}{344}]$ ........(2)

Since, the observer hears no beats, so $f_1=f_2$

Or $324[\frac{344-v_o}{344}]=$ $320[\frac{344+v_o}{344}]$

Or $324[344-v_o]=320[344+v_o]$

$⟹v_o=2.1m/s$