A boy riding on his bike is going towards east at a speed of $$42$$ $$m/s$$. At a certain point, he produces a sound pulse of frequency $$1650$$ Hz that travels in air at a speed of $$334$$ $$m/s$$ . A second boy stands on the ground $$450$$ south of east from him. The frequency of the pulse as received by the second boy is (in$$ $$Hz)

Question

A boy riding on his bike is going towards east at a speed of  $$42$$ $$m/s$$. At a certain point, he produces a sound pulse of frequency $$1650$$ Hz that travels in air at a speed of $$334$$ $$m/s$$ . A second boy stands on the ground  $$450$$ south of east from him. The frequency of the pulse as received by the second boy is (in$$ $$Hz)

Infinity Learn · Accepted Answer

$$1$$. Speed of boy  $$v=42$$ $$m/sFrequency$$ of sound pulse  $$v0=1650$$ $$HzB1$$ or the first boy is the source of the sound and  $$B2$$ is the listener. vs  is the component of the velocity of the source along the source – listener axis (SL$$ $$axis). Here,$$vs=42cos450=4$$ $$m/s$$  Using Doppler’s effect formula  $$v=v$$−vLv−$$vAv0Speed$$ of sound in $$airv=334$$ $$m/s$$, $$vs=4$$ $$m/s$$, $$vL=0$$ $$v=334334$$−$$4$$×$$1650$$ $$Hz=334330$$×$$1650$$ $$Hz=1670$$ HzTherefore, the correct answer is $$1670.00$$

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