A train is approaching a cliff at 10 m/s. The driver sounds a whistle of frequency 600 Hz. What will be the frequency of echo as heard by the driver? (Velocity of sound in air = 340[latex]ms^{-1}[/latex]).

Solution
Here,
Velocity of observer (v_o) = 10 m/s
Actual frequency of source (f) = 600 Hz
Apparent frequency of echo as heard by car driver (f’) =?
Velocity of sound in air = 340 m/s

We have,
The apparent frequency as heard by the driver is,
f ‘ = [latex](\frac{v+v_o}{v-v_s})f[/latex]

                        = [latex](\frac{340+10}{340-10})\times 600[/latex]

                        = 636.36 Hz.

A car is sounding a horn of frequency 500 Hz and travelling towards a stationary observer with speed 20 m/s. What is apparent frequency heard by the observer? (Velocity of sound in air = 340 m/s).

Solution

Given,
Frequency of source (f) = 500 Hz
Velocity of source (v_s) = 20 ms^-1
Apparent frequency as heard by observer ([latex]f'[/latex]) =?
Velocity of sound (v) = 340 m/s
As source is moving towards the stationary observer, the apparent frequency as heard by the observer is given by:
f’ = [latex]\frac{v}{v-v_s}\times f[/latex]
                        = [latex]\frac{340}{340-20}\times 500[/latex]
                        = 531.25 Hz

A car is approaching towards a cliff at a speed of 20 m/s. The driver sounds a whistle of frequency 800 Hz. What will be the frequency of the echo as heard by the car driver? [Velocity of sound in air = 350 m/s].

Solution

Here,

Velocity of observer ([latex]v_o[/latex]) = 20 m/s

Actual frequency of source (f) = 800 Hz

Apparent frequency of echo as heard by car driver (f’) =?