A police car is chasing a motorcyclist at a velocity of $$20m/s$$. velocity of motor cyclist is $$15m/s$$. Wind is blowing from the police car towards the motor cyclist with a velocity of $$30m/s$$ velocity of sound in still air is $$330m/s$$. If the motor cyclist blows horn of frequency $$400Hz$$, The apparent frequency of sound received by the police car is

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Infinity Learn · Accepted Answer

Apparent frequency $$f=f01+vmvs$$−$$vw1+vpvs$$−vw∴$$f=4001+15330$$−$$301+20330$$−$$30Hz=400$$×$$315320Hz=393.75Hz$$

Doppler

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Apparent frequency $f = \frac{f_{0} (1 + \frac{v_{m}}{v_{s} - v_{w}})}{(1 + \frac{v_{p}}{v_{s} - v_{w}})}$
$∴ f = \frac{400 (1 + \frac{15}{330 - 30})}{(1 + \frac{20}{330 - 30})} Hz = \frac{400 \times 315}{320} Hz = 393 .75 Hz$

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Doppler

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Apparent frequency f=f01+vmvs−vw1+vpvs−vw∴f=4001+15330−301+20330−30Hz=400×315320Hz=393.75Hz

Ready to Test Your Skills?

free study material

Apparent frequency $f = \frac{f_{0} (1 + \frac{v_{m}}{v_{s} - v_{w}})}{(1 + \frac{v_{p}}{v_{s} - v_{w}})}$
$∴ f = \frac{400 (1 + \frac{15}{330 - 30})}{(1 + \frac{20}{330 - 30})} Hz = \frac{400 \times 315}{320} Hz = 393 .75 Hz$