SATHEE: Wave Motion 4 Question 1

Wave Motion 4 Question 1

1. Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency $660 H z$ . A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed $u m / s$ and he hears 10 beats/s. The velocity of sound is $330 m / s$ . Then, $u$ equal to

(2019 Main, 12 April II)

(a) $5.5 m / s$

(b) $15.0 m / s$

(d) $10.0 m / s$

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Answer:

Correct Answer: 1. (c)

Solution:

When observer moves away from $S_{1}$ and towards $S_{2}$ ,

then due to Doppler’s effect observed frequencies of sources by observer are

$f_{S_{1}}^{'} = \frac{v - v_{o}}{v} \cdot f_{S_{1}}$

(observer moving away from source) and

$f_{S_{2}}^{'} = (\frac{v + v_{o}}{v}) \cdot f_{S_{2}}$

(observer moving towards source)

(where, $v =$ speed to sound, $v_{o} =$ speed of observer)

So, beat frequency heard by observer is

Here,

$\begin{aligned} f_{b} = f_{S_{2}}^{'} - f_{S_{1}}^{'} \\ v_{o} = u, v = 330 m s^{- 1} \\ f_{b} = 10 H z, f_{S_{1}} = f_{S_{2}} = 660 H z \end{aligned}$

On putting the values, we get

$\begin{aligned} f_{b} = f_{S_{2}}^{'} - f_{S_{1}}^{'} \\ = (\frac{v + v_{o}}{v}) \cdot f_{S_{2}} - (\frac{v - v_{o}}{v}) f_{S_{1}} \\ = f_{S_{1}} \frac{v + v_{o}}{v} - \frac{v - v_{o}}{v} = f_{S_{1}} \cdot \frac{2 v_{o}}{v} \\ \Rightarrow [∵ v_{o} = u] \\ \Rightarrow 10 = \frac{660 \times 2 u}{330} u = 2.5 m s^{- 1} \end{aligned}$

Wave Motion 4 Question 1

1. Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency $660 H z$ . A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed $u m / s$ and he hears 10 beats/s. The velocity of sound is $330 m / s$ . Then, $u$ equal to

Answer:

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Wave Motion 4 Question 1

1. 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 um/s and he hears 10 beats/s. The velocity of sound is 330m/s. Then, u equal to

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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1. Two sources of sound $S_{1}$ and $S_{2}$ produce sound waves of same frequency $660 H z$ . A listener is moving from source $S_{1}$ towards $S_{2}$ with a constant speed $u m / s$ and he hears 10 beats/s. The velocity of sound is $330 m / s$ . Then, $u$ equal to