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JEE MAIN 2022
26-07-2022 S1
Question
When a car is approaching the observer, the frequency of horn is 100 Hz. After passing the observer, it is 50Hz. If the observer moves with the car, the frequency will be $\frac{x}{3}$Hz where x = ___
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Solution
$\begin{aligned} & f_1=100=f_0\left(\frac{C}{C-V_s}\right) \\ & C=\text { speed of sound } \\ & V_s=\text { speed of source } \\ & f_2=50=f_0\left(\frac{C}{C+V_s}\right) \\ & \frac{f_1}{f_2}=2=\frac{C+V_s}{C-V_s} \\ & 2 C-2 V_s=C+V_s \\ & 3 V_s=C \\ & V_s=\frac{C}{3} \\ & 100=f_0 \frac{C}{\frac{2 C}{3}}=\frac{3}{2} f_0 \\ & f_0=\frac{200}{3}\end{aligned}$
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