Question

When a source of sound of frequency f crosses a stationary observer with a speed $v_S$(<< speed of sound v), the apparent change in frequency $△f$ is given by:

• A. $\frac{2f{v}_s}{v}$
• B. $\frac{2fv}{v_s}$
• C. $\frac{f{v}_s}{v}$
• D. $2fv{v}_s$

Answer 1

Answer: (A)

$\frac{2f{v}_s}{v}$

$Concept:$ When the source approaches the observer then there will be a frequency and when the source passes by the observer then there will be another frequency.

Let, the former frequency is $f_1$ and latter frequency is $f_2$

then $\Delta f=f_1-f_2$

$or,\Delta f=f\left(\frac{v}{v-v_s}\right)-f\left(\frac{v}{v+v_s}\right)$

$or,\Delta f=f(1-\frac{v_s}{v}{)}^{-1}-f(1+\frac{v_s}{v}{)}^{-1}$

$or,\Delta f=f(1+\frac{v_s}{v})-f(1-\frac{v_s}{v})$ [Using binomial expansion]

$or,\Delta f=f\left(\frac{2v_s}{v}\right)$

$or,\Delta f=\frac{2f{v}_s}{v}$

The correct answer is $OptionA:\frac{2f{v}_s}{v}$