Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u0 ms- 1 and he hears 10 beat s- 1 . The velocity of sound is 330 ms- 1. Then, u0 equals:

Question

Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from source S1 towards S2 with a constant speed u0 ms- 1 and he hears 10 beat s- 1 . The velocity of sound is 330 ms- 1. Then, u0 equals: (A) 10.0 ms- 1 (B) 2.5 ms- 1 (C) 5.5 ms- 1 (D) 15.0 ms- 1

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-b6jfxoh8yz2qhpbz.jpg" /> Frequency observed from S1: f1=660((330 - u0/330 - 0)) Frequency observed from S2: f2=660((330 + u0/330 - 0)) As f2-f1=10 660[(330 + u0/330 - 0) - (330 - u0/330 - 0)]=10 2(2 u0)=10 u0=2.5 ms- 1

Q. Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency $660 Hz .$ A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed $u_{0} m s^{- 1}$ and he hears $10 b e a t s^{- 1}$ . The velocity of sound is $330 m s^{- 1} .$ Then, $u_{0}$ equals:

$10.0 m s^{- 1}$

$2.5 m s^{- 1}$

$5.5 m s^{- 1}$

$15.0 m s^{- 1}$

Frequency observed from $S_{1} : f_{1} = 660 (\frac{330 - u _{0}}{330 - 0})$
Frequency observed from $S_{2} : f_{2} = 660 (\frac{330 + u _{0}}{330 - 0})$
As $f_{2} - f_{1} = 10$
$660 [\frac{330 + u _{0}}{330 - 0} - \frac{330 - u _{0}}{330 - 0}] = 10$
$2 (2 u_{0}) = 10$
$u_{0} = 2.5 m s^{- 1}$

Q. Two sources of sound S1​ and S2​ produce sound waves of same frequency 660Hz. A listener is moving from source S1​ towards S2​ with a constant speed u0​ms−1 and he hears 10beats−1 . The velocity of sound is 330ms−1. Then, u0​ equals:

10.0ms−1

2.5ms−1

5.5ms−1

15.0ms−1