   Chapter 14, Problem 1CQ

Chapter
Section
Textbook Problem

(a) You are driving down the highway in your car when a police car sounding its siren overtakes you and passes you. If its frequency at rest is f0, is the frequency you hear while the car is catching up to you higher or lower than f0? (b) What about the frequency you hear after the car has passed you?

(a)

To determine
The frequency of the siren heard by the observer while the car sounding its siren is catching up.

The frequency heard by you while the car is catching up is higher than the frequency f0 .

Explanation

The frequency of the car that is catching up can be found using the concept of Doppler effect. Doppler effect is the change in frequency heard by an observer whenever there is relative motion between a source of sound and the observer is called Doppler effect.

Formula for Doppler effect is,

fObs=f0(v+vOvvS)

• fObs is the frequency heard by you (observer).
• fS is the frequency of the Siren (source).
• v is the speed of air.
• vObs is the speed of your car(observer).
• vS is the speed of the police car (source).

The police car is catching you up. Relative to you, the police car is moving towards you while you are rest.

Substitute 0 for vO in the expression for Doppler effect to find fObs .

fObs=f0(v+0vvS)=f0(vvvS)

The numerator contains v term and denominator contains vvs term. The numerator is larger than the denominator. Hence, the observed frequency is greater than the frequency of the source.

Conclusion: The frequency heard by you while the car is catching up is higher than the frequency f0 .

(b)

To determine
The frequency of the siren heard by you while the car sounding its siren is passes away.

The frequency heard by the you after the car passed you is lesser than the frequency f0 .

Explanation

The police car is move past you. Relative to you, the police car is moving away from you while you are rest.

When the source moves away from the observer, negative speed is substituted for vS .

Substitute 0 for vO and (vS) for vS   in the expression for Doppler effect to find fObs .

fObs=f0(v+0v(vS))=f0(vv+vS)

The numerator contains v term and denominator contains v+vs term. The numerator is smaller than the denominator. Hence, the observed frequency is smaller than the frequency of the source.

Conclusion: The frequency heard by the you after the car passed you is lesser than the frequency f0 .

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