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17.4 Doppler effect and sonic booms  (Page 5/9)

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Photograph of a black duck swimming in water. The path left behind by the duck in water shows a near cone shape.
Bow wake created by a duck. Constructive interference produces the rather structured wake, while there is relatively little wave action inside the wake, where interference is mostly destructive. (credit: Horia Varlan, Flickr)
Photograph of the blue glow, in a research reactor pool.
The blue glow in this research reactor pool is Cerenkov radiation caused by subatomic particles traveling faster than the speed of light in water. (credit: U.S. Nuclear Regulatory Commission)

Doppler shifts and sonic booms are interesting sound phenomena that occur in all types of waves. They can be of considerable use. For example, the Doppler shift in ultrasound can be used to measure blood velocity, while police use the Doppler shift in radar (a microwave) to measure car velocities. In meteorology, the Doppler shift is used to track the motion of storm clouds; such “Doppler Radar” can give velocity and direction and rain or snow potential of imposing weather fronts. In astronomy, we can examine the light emitted from distant galaxies and determine their speed relative to ours. As galaxies move away from us, their light is shifted to a lower frequency, and so to a longer wavelength—the so-called red shift. Such information from galaxies far, far away has allowed us to estimate the age of the universe (from the Big Bang) as about 14 billion years.

Why did scientist Christian Doppler observe musicians both on a moving train and also from a stationary point not on the train?

Doppler needed to compare the perception of sound when the observer is stationary and the sound source moves, as well as when the sound source and the observer are both in motion.

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Describe a situation in your life when you might rely on the Doppler shift to help you either while driving a car or walking near traffic.

If I am driving and I hear Doppler shift in an ambulance siren, I would be able to tell when it was getting closer and also if it has passed by. This would help me to know whether I needed to pull over and let the ambulance through.

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Test prep for ap courses

A baggage handler stands on the edge of a runway as a landing plane approaches. Compared to the pitch of the plane as heard by the plane’s pilot, which of the following correctly describes the sensation experienced by the handler?

  1. The frequency of the plane will be lower pitched according to the baggage handler and will become even lower pitched as the plane slows to a stop.
  2. The frequency of the plane will be lower pitched according to the baggage handler but will increase in pitch as the plane slows to a stop.
  3. The frequency of the plane will be higher pitched according to the baggage handler but will decrease in pitch as the plane slows to a stop.
  4. The frequency of the plane will be higher pitched according to the baggage handler and will further increase in pitch as the plane slows to a stop.

(c)

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The following graph represents the perceived frequency of a car as it passes a student.

A graph of time in seconds on the x-axis versus perceived frequency in hertz on the y-axis. The line is flat at 218 hertz from 0 to about 0.5 seconds, then declines linearly from (0.5, 218) to (0.8, 181), and then is flat at 181 hertz until the line ends.
Plot of time versus perceived frequency to illustrate the Doppler effect.
  1. If the true frequency of the car’s horn is 200 Hz, how fast was the car traveling?
  2. On the graph above, draw a line demonstrating the perceived frequency for a car traveling twice as fast. Label all intercepts, maximums, and minimums on the graph.
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Section summary

  • The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer.
  • The actual change in frequency is called the Doppler shift.
  • A sonic boom is constructive interference of sound created by an object moving faster than sound.
  • A sonic boom is a type of bow wake created when any wave source moves faster than the wave propagation speed.
  • For a stationary observer and a moving source, the observed frequency f obs size 12{f rSub { size 8{"obs"} } } {} is:
    f obs = f s v w v w ± v s , size 12{f rSub { size 8{"obs"} } =f rSub { size 8{s} } left ( { {v rSub { size 8{w} } } over {v rSub { size 8{w} } +- v rSub { size 8{s} } } } right )} {}
    where f s size 12{f rSub { size 8{s} } } {} is the frequency of the source, v s size 12{v rSub { size 8{s} } } {} is the speed of the source, and v w size 12{v rSub { size 8{w} } } {} is the speed of sound. The minus sign is used for motion toward the observer and the plus sign for motion away.
  • For a stationary source and moving observer, the observed frequency is:
    f obs = f s v w ± v obs v w , size 12{f rSub { size 8{"obs"} } =f rSub { size 8{s} } left ( { {v rSub { size 8{w} } +- v rSub { size 8{"obs"} } } over {v rSub { size 8{w} } } } right )} {}
    where v obs size 12{v rSub { size 8{"obs"} } } {} is the speed of the observer.

Conceptual questions

Is the Doppler shift real or just a sensory illusion?

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Due to efficiency considerations related to its bow wake, the supersonic transport aircraft must maintain a cruising speed that is a constant ratio to the speed of sound (a constant Mach number). If the aircraft flies from warm air into colder air, should it increase or decrease its speed? Explain your answer.

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When you hear a sonic boom, you often cannot see the plane that made it. Why is that?

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Problems&Exercises

(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?

(a) 878 Hz

(b) 735 Hz

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(a) At an air show a jet flies directly toward the stands at a speed of 1200 km/h, emitting a frequency of 3500 Hz, on a day when the speed of sound is 342 m/s. What frequency is received by the observers? (b) What frequency do they receive as the plane flies directly away from them?

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What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s.

3.79 × 10 3 Hz

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A spectator at a parade receives an 888-Hz tone from an oncoming trumpeter who is playing an 880-Hz note. At what speed is the musician approaching if the speed of sound is 338 m/s?

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A commuter train blows its 200-Hz horn as it approaches a crossing. The speed of sound is 335 m/s. (a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train? (b) What frequency does the observer receive as the train moves away?

(a) 12.9 m/s

(b) 193 Hz

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Can you perceive the shift in frequency produced when you pull a tuning fork toward you at 10.0 m/s on a day when the speed of sound is 344 m/s? To answer this question, calculate the factor by which the frequency shifts and see if it is greater than 0.300%.

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Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?

First eagle hears 4.23 × 10 3 Hz

Second eagle hears 3.56 × 10 3 Hz

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What is the minimum speed at which a source must travel toward you for you to be able to hear that its frequency is Doppler shifted? That is, what speed produces a shift of 0.300% on a day when the speed of sound is 331 m/s?

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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