Question

A source of sound moving with speed 30 ms
-1
away from an observer emits a
sound of frequency 500 Hz. Calculate the frequency observed by an observer
moving with a speed 25 ms towards the source. The speed of sound is
340 ms -1
-1​

Answer 1

Given:

Sound source moving with speed of 30 m/s away from an observer emits a sound of frequency 500 Hz. The observer is moving towards the source with a speed of 25 m/s. Speed of sound is 340 m/s.

To find:

The apparent frequency heard by observer.

Concept:

We shall apply Doppler's Effect to calculate the apparent frequency heard by the observer. This happens due to relative displacement between the source and observer .

Calculation:

Let apparent frequency be f ;

$\therefore \: f = \bigg \{\dfrac{v +v_{o}}{v +v_{s} } \bigg \} \times 500$

$= > \: f = \bigg \{\dfrac{340 +25}{340 + 30} \bigg \} \times 500$

$= > \: f = \bigg \{\dfrac{365}{370} \bigg \} \times 500$

$= > f = 0.986 \times 500$

$= > f = 493.24 \: hz$

So the apparent frequency heard by the oberver is lesser than the original frequency of the source.

So , final answer is :

$\boxed{ \red{ \huge{ \bold{f = 493.24 \: hz}}}}$

Answer 2

A source of sound is travelling with a velocity of 30ms towards a stationary observer. If actual frequency of source is 1000 Hz and the wind is blowing with velocity 20ms in a direction at 60∘C with the direction of motion of source, then the apparent frequency heard by observer is (speed of sound is 340ms).