A motor cycle starts from rest and accelerates along a straight path at $$2m/s2$$ .At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $$94$$% of its value when the motor cycle was at rest? (speed$$ of sound $$=330ms$$−$$1$$ $$)

Question

A motor cycle starts from rest and accelerates along a straight path at $$2m/s2$$ .At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $$94$$% of its value when the motor cycle was at rest? (speed$$ of sound $$=330ms$$−$$1$$ $$)

Infinity Learn · Accepted Answer

$$v2m$$−$$u2=2as$$∴$$v2m=2$$×$$2s$$   $$vm=2sAccording$$ to Doppler’s effectv′$$=vv$$−vmv $$0.94v=v330$$−$$2s330$$ ⇒$$s=98.01$$

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