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Chapter 16: Problem 3

A police car is moving in your direction, constantly accelerating, with its siren on. As it gets closer, the sound you hear will a) stay at the same frequency. b) drop in frequency. c) increase in frequency. d) More information is needed.

Short Answer

Expert verified
Answer: The frequency of the siren will experience an increase in frequency due to the Doppler effect as the police car is accelerating towards you.

Step by step solution

01

Understand the Doppler effect

The Doppler effect occurs when there is a change in the frequency of a wave due to the relative motion between the wave source and the observer. The Doppler effect formula for sound waves is given by: f' = f (v + vₒ) / (v + vₛ) where f' is the observed frequency, f is the emitted frequency, v is the speed of sound in the medium, vₒ is the speed of the observer, and vₛ is the speed of the source. Here, the observer is stationary, so vₒ = 0. The police car is the source, and it is accelerating, which means its speed is increasing with time.
02

Determine the direction of the Doppler effect

When the source is moving towards the observer (positive acceleration) while the observer is stationary, the Doppler effect causes an increase in frequency. When the source is moving away from the observer, the Doppler effect causes a decrease in frequency. In this exercise, the police car is moving towards you, meaning the Doppler effect will cause an increase in the observed frequency.
03

Identify the correct answer

Now that we know the Doppler effect for the accelerating police car will lead to an increased observed frequency, the correct answer is: c) increase in frequency.

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