Question

Two aeroplanes A and B are moving away from
one anothers with a speed of 720 kmph. The frequency
of the whistle emitted by A is 1100 Hz. calculate
the apparent frequency of the whistle as heard by
the passenger of the aeroplane "B!? (velocity of sound
in air is 350 mls.)​

Answer 1

Given :

Two aeroplanes A and B are moving away from one another with a speed of 720kmph.

• 720kmph = 720 × 5/18 = 200mps

Original frequency = 1100Hz

Velocity of sound = 350m/s

To Find :

Apparent frequency of the whistle.

Solution :

❒ Apparent frequency of a sound heard by listener, when source and listener are moving away from each other, then

$:\implies\:\underline{\boxed{\bf{\pink{f'=\bigg(\dfrac{v-v_l}{v+v_s}\bigg)\times f}}}}$

• f' denotes apparent frequency
• f denotes original frequency
• v denotes velocity of sound
• $\sf{v_s}$ denotes velocity of source
• $\sf{v_l}$ denotes velocity of listener

By substituting the given values;

$\sf:\implies\:f'=\bigg(\dfrac{v-v_l}{v+v_s}\bigg)\times f$

$\sf:\implies\:f'=\bigg(\dfrac{350-200}{350+200}\bigg)\times 1100$

$\sf:\implies\:f'=\bigg(\dfrac{150}{550}\bigg)\times 1100$

$\sf:\implies\:f'=0.27\times 1100$

$:\implies\:\underline{\boxed{\bf{\purple{f'=297\:Hz}}}}$