JEE Advanced 2021 · Paper 2 · Physics Q2

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PhysicsMultiple correct+4 / -2Question 2 of 57

A source, approaching with speed $u$ towards the open end of a stationary pipe of length $L$ , is emitting a sound of frequency $f_s$ . The farther end of the pipe is closed. The speed of sound in air is $v$ and $f_0$ is the fundamental frequency of the pipe. For which of the following combination(s) of $u$ and $f_s$ , will the sound reaching the pipe lead to a resonance?

u = 0.8v

and

f_s = f_0

u = 0.8v

and

f_s = 2f_0

u = 0.8v

and

f_s = 0.5f_0

u = 0.5v

and

f_s = 1.5f_0

Answer and worked solution

Official answer: A, D

Resonances. A pipe closed at one end resonates only at odd multiples of its fundamental: $f_0,\,3f_0,\,5f_0,\dots$

Frequency reaching the pipe (moving source): $f'=f_s\dfrac v{v-u}$ .

Check each option.

(A) $u=0.8v$ : $f'=5f_s=5f_0$ . Resonance.
(B) $f'=10f_0$ , an even multiple. No resonance.
(C) $f'=2.5f_0$ . No resonance.
(D) $u=0.5v$ : $f'=2f_s=3f_0$ . Resonance.

(A), (D)

Topics:Doppler effect Organ pipes and resonance

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JEE Advanced 2021 · Paper 2, Physics question 2