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

Two stationary sources each emit waves of wavelength $\lambda$. An observer moves from one source to the other with velocity $u$. The number of beats heard by the observer is:

$A$ boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed as the train approaches and recedes him with a velocity of $108 \text{ km/h}$ is (speed of sound in air $= 330 \text{ m/s}$) (in $\%$)

$A$ sound source $S$ is moving along a straight track with speed $v,$ and is emitting sound of frequency $v_{0}.$ An observer is standing at a finite distance,at the point $O,$ from the track. The time variation of frequency heard by the observer is best represented by (where $t_{0}$ represents the instant when the distance between the source and observer is minimum).

$A$ source of sound is travelling at $\frac{100}{3} \, m/s$ along a road,towards a point $A$. When the source is $3 \, m$ away from $A$,a person is standing at a point $O$ on a road perpendicular to the path of the source. The distance of $O$ from $A$ at that time is $4 \, m$. If the original frequency is $640 \, Hz$,then the apparent frequency heard by the person is ...... $Hz$ (speed of sound is $340 \, m/s$).

$A$ train is moving on a straight track with speed $20 \ ms^{-1}$. It is blowing its whistle at a frequency of $1000 \ Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $= 320 \ ms^{-1}$) close to .... $\%$

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