JEE Main 2015 · 11 Apr · Shift 1 · Physics Q13

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PhysicsSingle correct+4 / -1Question 13 of 90

A source of sound emits sound waves at frequency $f_0$ . It is moving towards an observer with fixed speed $v_s$ ( $v_s<v$ , where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$ , one of the following two graphs (A and B) will give the correct variation of the frequency f heard by the observer as $v_0$ is changed.

The variation of f with $v_0$ is given correctly by :

Graph A: f against v₀, a straight line with positive intercept and positive slope. Graph B: f against 1/v₀, also a straight rising line.

graph A with slope

=\dfrac{f_0}{(v-v_s)}

graph A with slope

=\dfrac{f_0}{(v+v_s)}

graph B with slope

=\dfrac{f_0}{(v-v_s)}

graph B with slope

=\dfrac{f_0}{(v+v_s)}

Answer and worked solution

Official answer: A

$f=f_0\frac{v+v_0}{v-v_s}=\frac{f_0v}{v-v_s}+\frac{f_0}{v-v_s}v_0.$
This is linear in $v_0$ with a positive intercept: graph A, with slope $\dfrac{f_0}{v-v_s}$ .

Topics:Doppler effect

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JEE Main 2015 · 11 Apr · Shift 1, Physics question 13