A stationary observer receives sound from two | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let $c$ be the speed of sound and $v$ be the speed of the tuning forks.The frequency heard from the approaching tuning fork is $
u_{1} = \left(\f

Vedclass · Accepted Answer

$\frac{1}{4} \; 	ext{m/s}$

Vedclass · Answer

(D) Let $c$ be the speed of sound and $v$ be the speed of the tuning forks.The frequency heard from the approaching tuning fork is $
u_{1} = \left(\frac{c}{c-v}ight) 
u_{0}$.The frequency heard from the receding tuning fork is $
u_{2} = \left(\frac{c}{c+v}ight) 
u_{0}$.The beat frequency is given by $\Delta 
u = 
u_{1} - 
u_{2} = 2 \; 	ext{Hz}$.Substituting the expressions:$\Delta 
u = c 
u_{0} \left(\frac{1}{c-v} - \frac{1}{c+v}ight) = c 
u_{0} \left(\frac{c+v - (c-v)}{c^{2}-v^{2}}ight) = \frac{2 c 
u_{0} v}{c^{2}-v^{2}}$.Since $v \ll c$, we can approximate $c^{2} - v^{2} \approx c^{2}$.Thus, $\Delta 
u \approx \frac{2 c 
u_{0} v}{c^{2}} = \frac{2 
u_{0} v}{c} = 2$.Substituting the given values: $\frac{2 	imes 1400 	imes v}{350} = 2$.$8v = 2 \Rightarrow v = \frac{2}{8} = \frac{1}{4} \; 	ext{m/s}$.

Similar Questions

$A$ car sounding a horn of frequency $1000 \ Hz$ passes a stationary observer. The ratio of the frequencies of the horn noted by the observer before and after the passing of the car is $11 : 9$. If the speed of sound is $v$,what is the speed of the car?

The pitch of a whistle of an engine appears to drop by $30 \%$ of its original value when it passes a stationary observer. If the speed of sound in air is $350 \ m/s$,then the speed of the engine in $m/s$ is:

$A$ driver in a car,approaching a vertical wall,notices that the frequency of his car horn has changed from $440 \, Hz$ to $480 \, Hz$ when it gets reflected from the wall. If the speed of sound in air is $345 \, m/s,$ then the speed of the car is $....... \, km/hr$.

When both the source of sound and the observer approach each other with a speed equal to $10 \%$ of the speed of sound,then the percentage change in frequency heard by the observer is nearly (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module