An observer moves towards a stationary source of sound, with a...

An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?

Options

AZero
B $0.5 \%$
C $5 \%$
D $20 \%$

Correct answer

D. $20 \%$

Step-by-step solution

Given :

v_o=\frac{v}{5} \Rightarrow v_o=\frac{320}{5}=64 \mathrm{~m} / \mathrm{s}

When observer moves towards the stationary source, then

\begin{aligned} n^{\prime} & =\left(\frac{v+v_0}{v}\right) n \\ n^{\prime} & =\left(\frac{320+64}{320}\right) n \\ n^{\prime} & =\left(\frac{384}{320}\right) n \\ \frac{n^{\prime}}{n} & =\frac{384}{320} \end{aligned}

Hence, percentage increase

\begin{aligned} \left(\frac{n^{\prime}-n}{n}\right) & =\left(\frac{384-320}{320} \times 100\right) \% \\ & =\left(\frac{64}{320} \times 100\right) \%=20 \% \end{aligned}

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