When the source of sound moves away from a stationary listener,we obtain $f_{L} < f_{S}$. Why?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The general formula for the Doppler effect is given by $\frac{f_{L}}{v + v_{L}} = \frac{f_{S}}{v + v_{S}}$,where $v$ is the speed of sound,$v_{L}$ is the velocity of the listener,and $v_{S}$ is the velocity of the source.
Given that the listener is stationary,$v_{L} = 0$.
When the source moves away from the listener,the velocity of the source $v_{S}$ is taken as positive in the direction of sound propagation (from listener to source),so the denominator becomes $(v + v_{S})$.
Substituting these values,we get $\frac{f_{L}}{v + 0} = \frac{f_{S}}{v + v_{S}}$.
Therefore,$f_{L} = \left( \frac{v}{v + v_{S}} \right) f_{S}$.
Since $v + v_{S} > v$,the fraction $\frac{v}{v + v_{S}} < 1$. Consequently,$f_{L} < f_{S}$.

Explore More

Similar Questions

An engine sounding a whistle of frequency $1152 \ Hz$ is receding from a stationary observer at $72 \ km/h$. If the velocity of sound in air is $340 \ m/s$,then the frequency of the note heard by the observer is: (in $Hz$)

An observer is approaching with a speed $v$ towards a stationary source emitting sound waves of wavelength $\lambda_0$. The wavelength shift detected by the observer is (Take $c$ as the speed of sound).

An engine is moving towards a wall with a velocity $50\, ms^{-1}$ and emits a note of $1.2\, kHz$. The speed of sound in air is $350\, ms^{-1}$. The frequency of the note after reflection from the wall as heard by the driver of the engine is ..... $kHz$.

Difficult
View Solution

$A$ car moving towards a cliff emits sound of frequency '$n$'. If the difference in frequencies of the horn and its echo heard by the driver of the car is $10 \%$ of '$n$',then the speed of the car is nearly (Speed of sound in air is $336 \ m/s$) (in $m/s$)

$A$ railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer standing beside the railway track. The frequency $(n)$ of the sound heard by the observer is plotted against time $(t).$ Which of the following best represents the resulting curve?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo