Doppler effect on a police car?

In summary, the frequency of the wave emitted by the police car's siren decreases from 60 Hz to 51.4 Hz as it travels away from a stationary observer at a speed of 300 m/s. The wavelength of the wave behind the car is calculated to be 5.8 meters. However, according to the book, the final frequency is stated to be 70 Hz. It seems that one of the equations used may be incorrect.
  • #1
MCATPhys
58
0
A police car's siren emits a wave with a frequency of 60 Hz. The speed of sound is 300 m/s and the car is moving 50 m/s. "what is the wavelength of the wave behind the car"

So, the answer seems pretty easy. The observer is a stationary point behind the car, and the source is moving away from the observer, which means frequency should decrease:

f = 60 (300+0)/(300+50) = 51.4 Hz
wavelength = 300/51.4 = 5.8

Is this logic correct?

However, the answer in the book states that the final frequency is 70 Hz, by this equation:
f = 60 (300+50)/(300+0) = 70 Hz

Which one is correct?
 
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  • #2
An increase in the frequency would indeed make no sense at all. :)
 

Related to Doppler effect on a police car?

1. How does the Doppler effect impact the sound of a police car siren?

The Doppler effect describes the change in frequency of a wave when the source of the wave is moving. In the case of a police car siren, as the car moves towards an observer, the sound waves are compressed, resulting in a higher frequency and a higher pitch. As the car moves away from the observer, the sound waves are stretched, resulting in a lower frequency and a lower pitch. This change in frequency is what creates the characteristic "wailing" sound of a police siren.

2. Why does a police car siren sound different when it is moving towards me compared to when it is moving away from me?

This is due to the Doppler effect, as explained above. When the police car is moving towards you, the sound waves are compressed, resulting in a higher frequency and a higher pitch. When the car is moving away from you, the sound waves are stretched, resulting in a lower frequency and a lower pitch. This change in pitch is what creates the difference in sound that you hear.

3. Can the Doppler effect be observed with other types of waves besides sound waves?

Yes, the Doppler effect can be observed with all types of waves, including light waves, water waves, and even seismic waves. In the case of light waves, the change in frequency is what causes the phenomenon known as "redshift" in astronomy, where objects that are moving away from us appear redder than they actually are.

4. How does the speed of the police car affect the Doppler effect on the siren?

The speed of the police car does not have a direct effect on the Doppler effect on the siren. However, the speed of the car does impact the rate at which the frequency of the siren changes. The faster the car is moving, the more quickly the frequency will change, resulting in a more dramatic shift in pitch.

5. Can the Doppler effect be used by law enforcement for purposes other than sirens on police cars?

Yes, the Doppler effect has many practical applications in law enforcement. For example, it can be used in radar guns to measure the speed of moving vehicles, and it is also used in ultrasound technology for detecting moving objects within the body, such as a fetus during pregnancy. Additionally, the Doppler effect is used in sonar technology for detecting underwater objects, which is often used by law enforcement for search and rescue operations.

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