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When a car is approaching the observer, the frequency of horn is $100 \mathrm{~Hz}.$ After passing the observer, it is $\mathrm{50 \mathrm{~Hz}.}$ If the observer moves with the car, the frequency will be $\mathrm{\frac{x}{3} \mathrm{~Hz}}$ where $\mathrm{x=}$ ___________.
Option: 1
200

Option: 2
-

Option: 3
-

Option: 4
-

Answers (1)

best_answer

Let the frequency of horn be fo

Case I

$\mathrm{f_{1}=f_{0}\left ( \frac{v}{v-v_{s}} \right )}$

$\mathrm{100=f_{0}\left ( \frac{v}{v-v_{s}} \right )}\rightarrow (1)$

Case II

$\mathrm{f_{2}=50=f_{0}\left ( \frac{v}{v+v_{s}} \right )}\rightarrow (2)$

Case III

When the observer moves with car,he will hear the original frequency $\mathrm{f}$

$\mathrm{f_0=\frac{x}{3}}$

From eq (1) & (2)

$\mathrm{ \frac{100}{50}=\frac{V+V_s}{V-V_s}}$

$\mathrm{2\left(v-v_s\right)=v+v_s}$

$\mathrm{V=3 V_s}$

$\mathrm{100=f_0\left(\frac{3 V_s}{3 V_s-V_s}\right)}$

$\mathrm{f_0=\frac{200}{3} \mathrm{~Hz}}$

$\mathrm{\therefore x=200}$

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