A police siren emits a sound somewhere around 700 Hz. If you are waiting at a red light, and a police car approaches you from behind and passes you, moving at a constant 30 m/s, what is the frequency you hear from the siren as it approaches you from behind? What about once it's passed you? Assume the air temperature to be 20°C.
18. Waves & Sound
The Doppler Effect
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A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h. What siren frequencies are heard in a car traveling at 90.0 km/h in the opposite direction before and after passing the police car?
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A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?
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A railroad train is traveling at 30.0 m/s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m/s and receding from the first?
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Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultrasound off a fetus in the womb. Consider an object moving at speed vo toward an at-rest source that is emitting sound waves of frequency f0. Show that the reflected wave (i.e., the echo) that returns to the source has a Doppler-shifted frequency fecho = (v+v0 / v-v0) f0 where v is the speed of sound in the medium.
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(II) A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 22.0 m/s. What is the received sound frequency?
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The siren of a fire engine that is driving northward at 30.0 m/s emits a sound of frequency 2000 Hz. A truck in front of this fire engine is moving northward at 20.0 m/s. (a) What is the frequency of the siren's sound that the fire engine's driver hears reflected from the back of the truck?
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A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading south). What frequency is heard by a cyclist heading north, toward the whistle at 12.0 m/s? Assume T = 20 °C .
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(II) Two trains emit 508-Hz whistles. One train is stationary. The conductor on the stationary train hears a 4.5-Hz beat frequency when the other train approaches. What is the speed of the moving train?
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A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 85 m, what is the minimum time between pulses (in fresh water)?
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A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h. The police car passes a car traveling in the same direction at 80.0 km/h. What two frequencies are heard in this car?
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A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading south). What frequency will observers hear who are located, at rest, due east, of the whistle?