12.3 The Doppler Effect

Transcription

1 12.3 The Doppler Effect

2 Doppler Effect Fire engine doppler effect video Car doppler effect video

3 Doppler Effect The pitch (frequency) of the horn of a passing car changes from high to low. This is due to the Doppler effect, named after Christian Doppler ( ) who first studied it scientifically (with regard to trains). The Doppler effect occurs when the velocity of the sound source---or of the observer---is a significant fraction of the velocity of the waves themselves.

4 The Doppler Effect: Description When a sound source moves toward an observer, the frequency heard is higher than the frequency produced by the source. When a sound source moves away from an observer, the frequency heard is lower than the frequency produced by the source.

5 The Doppler Effect t = 0: Sound source emitting 1 st wave crest: t = T 0 : Sound source emitting 2 nd wave crest: v s λ new = v w T 0 + v s T 0 v w f new = v w+ v s f 0 f new = 1 + f 0 v s v w wavelength increases frequency decreases λ new = v w T 0 v s T 0 v w f new = v w v s f 0 f new = 1 f 0 v s v w wavelength decreases frequency increases

6 The Doppler Effect So the frequency heard depends on the motion of the sound source relative to the observer.

7 Moving Observer A stationary sound source with a moving observer will also cause a Doppler effect. Here the wavelength is the original but the apparent velocity is not. For an observer moving toward a source: f new = v new = v s + v obs = v s + v obs f 0 λ λ v s f new = 1 + v obs v s f 0

8 Doppler Effect: General Form If both the sound source and the observer are moving: f obs = 1 ± v obs v wave f 1 ± v source v 0 wave What signs to use? If the observer is moving toward the source, or the source toward the observer, the pitch will be higher: use + v obs or v source. If the observer is moving away from the source, or the source away from the observer, the pitch will be lower: use v obs or + v source.

9 Example 1 An express train sounds its whistle as it approaches a station. If the whistle s pitch is 655 Hz and the train s speed is 21.2 m/s, what is the frequency heard by an observer at the station? f obs = 1 ± v obs v wave f 1 ± v source v 0 wave f obs = m s Hz 343 m s 1 f obs = 698 Hz

10 Example 2 A street musician sounds the A string on his violin at Hz. What frequency does a bicyclist hear as she moves away at 11.0 m/s? f obs = 1 ± v obs v wave f 1 ± v source v 0 wave f obs = m s m s f obs = 426 Hz 440 Hz

11 The Doppler Effect: Light The Doppler effect also occurs for electromagnetic waves. The frequency of light waves coming from distant galaxies is slightly higher ( redder ) than that typical for stars, indicating that they are moving away from us at a significant fraction of the speed of light. In fact, the velocity of galaxies and stars can be estimated from their amount of red-shift (or blue-shift, if moving toward us).

12 Doppler Effect: Applications The Doppler effect is used with radio waves to estimate the speed of cars, baseballs and winds based on the frequency of the reflected waves. The amplitude of the reflected radar wave tells the number of rain drops; the Doppler shift tells their horizontal velocity.

13 Shock Wave / Sonic Boom For the leading edge of a moving sound source: 1 f obs = f 1 v source v 0 wave What happens when v source v wave = 343 m/s? No sound is heard on approach, then a sonic boom occurs: a sound of large amplitude due to the constructive interference of multiple wave crests.

14 Shock wave physics video Sonic boom video

15 Supersonic Speeds An object, such as an airplane, moving at supersonic speed---faster than the speed of sound---is given a Mach number: Mach number = v object v sound A conical shock wave is produced, which is heard by an observer as a sonic boom, which may contain enough energy to break windows and cause other damage.

16 Shock Waves Shock waves are analogous to the bow waves produced by a boat going faster than the speed of the water waves it produces.

17 A Boat s wake A bit more complicated though the wake does have an amplified leading crest.

18 Shock Wave Angle The shock wave is a cone with its apex at the moving object. The angle of this cone is given by sin θ = v wave v object

19 A Boat s wake The angle and amplitude of the wake are also related to the speed of the boat.

20 Ultrasonic and Infrasonic Sound waves can have any frequency; the human ear can hear sounds between about 20 Hz and 20,000 Hz. Sounds with frequencies greater than 20,000 Hz are called ultrasonic; sounds with frequencies less than 20 Hz are called infrasonic. Elephants and whales communicate, in part, by infrasonic waves. Ultrasonic waves are used in medical applications.

21 Applications: Sonar, Ultrasound, and Medical Imaging The reflection of sound is used in many applications to determine the distance and the spatial structure of objects, by measuring the time it takes a sound pulse to reflect back to the receiver. Changes in amplitude indicate changes in density. Ultrasonic waves are often used, as the shorter wavelengths have less diffraction relative to objects and thus allow the sensing of smaller objects.

22 Echolocation Bats, whales and dolphins use echolocation to find prey.

23 Sonar Sonar (SOund NAvigation Ranging) is used to locate objects underwater, and the depth an features of the sea floor. Similar techniques can be used to learn about the internal structure of the Earth, including the location of oil deposits.

24 Ultrasound and Medical Imaging Ultrasound sonograms are used in medicine, such as to detect tumors or pockets of fluid, or to monitor the health of a fetus.