Question

The difference between the apparent frequencies of a source of sound as perceived by a stationary observer during its approach and recession is 2% of the actual frequency of the source. If the speed of sound is 300 m/s, the speed of source is

• A. 1.5 m/s
• B. 3 m/s
• C. 6 m/s
• D. 12 m/s

Answer 1

The correct option is B 3 m/s

$\frac{f_{approach}-f_{recode}}{f}=\frac{\Delta f}{f}=\frac{v}{v-v_s}-\frac{v}{v+v_s}\therefore \frac{\Delta f}{f}=\frac{v(v+v_s-v+v_s)}{v^2-v_s^2}=\frac{2v{v}_s}{v^2-v_s^2}$
$But\frac{\Delta f}{f}\times 100=2\%\Rightarrow 0.02=\frac{2\left(300\right)v_s}{(300{)}^2-v_s^2}\Rightarrow 0.02=\frac{2\left(300\right)v_s}{(300{)}^2}=\frac{2}{300}{v}_s\therefore v_s=\left(0.01\right)300=3m/s$