Question

What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? \{Speed of sound wave is $\mathrm{v}\}$ (A) $\mathrm{v}$ (B) $2 \mathrm{v}$ (C) $\mathrm{v} / 2$ (D) $\mathrm{v} / 4$

Name: Problem 1455, Chapter 10: JEE Physics
Uploaded: 2021-11-12T15:28:05-08:00
Duration: 1 min 26 s
Channel: Akshaya Rs
Description: What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? {Speed of sound wave is v} (A) v (B) 2 v (C) v / 2 (D) v / 4

   What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? \{Speed of sound wave is $\mathrm{v}\}$
(A) $\mathrm{v}$
(B) $2 \mathrm{v}$
(C) $\mathrm{v} / 2$
(D) $\mathrm{v} / 4$

JEE Physics

StemEZ 1st Edition

Chapter 10, Problem 1455

Instant Answer

Solved by Expert Akshaya Rs

11/12/2021

Step 1

Step 1: The apparent frequency $f'$ heard by the listener due to the Doppler effect is given by the formula: \[f' = \frac{{(v + v_0)}}{v} f\] where $v$ is the speed of sound, $v_0$ is the speed of the source, and $f$ is the actual frequency of the sound produced by Show more…

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What should be the speed of a source of sound moving towards a stationary listener, so that the frequency of sound heard by the listener is double the frequency of sound produced by the source? \{Speed of sound wave is $\mathrm{v}\}$ (A) $\mathrm{v}$ (B) $2 \mathrm{v}$ (C) $\mathrm{v} / 2$ (D) $\mathrm{v} / 4$

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Key Concepts

Doppler Effect

The Doppler effect is the phenomenon where the observed frequency of a wave changes due to the relative motion between the source of the wave and the observer. For sound waves, when the source moves towards a stationary listener, the waves are compressed, leading to a higher observed frequency than the one emitted.

Frequency Shift Calculation

In the context of the Doppler effect for sound, the frequency perceived by a stationary listener when the source is moving can be calculated using the formula f' = f / (1 - (v_source / v_sound)). Setting the observed frequency to be twice the emitted frequency leads to an equation that can be solved for the source’s speed, illustrating how the relative velocity impacts the perceived frequency.

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