LECTURE 8 DOPPLER EFFECT

Instructor: Kazumi Tolich Lecture 8

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¨ 15.7 The Doppler effect ¤ from a moving source ¤ A stationary source and a moving observer ¤ The Doppler effect for light waves ¤ shift on reflection from a moving object 15.7 The Doppler effect

¨ The Doppler effect is a change in frequency due to the motion of the source or observer. ¤ This effect is heard as the pitch of an ambulance siren changes from its approach to after it has passed you by. Quiz: 15.7-1

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¨ Which of the following shows fronts of sound wave emitted from a source moving to the right at a constant speed?

A B C D E Quiz: 15.7-1 answer

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¨ Which of the following shows wave fronts of sound wave emitted from a source moving to the right at a constant speed?

B Quiz: 15.7-2

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¨ Observers A, B, and C listen to a sound form a moving source. The locations of the sound wave crests at a given moment are shown in the figure. Rank the observer according to the frequency of the sound, smallest first. Quiz: 15.7-2 answer

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¨ A < B < C

¨ The of the sound wave is indicated by the distance between two neighboring crests.

¨ At C, the crests are closer together, indicating the smaller wavelength. ¨ Thus the observed frequency is highest at C since � = , where � is the speed of the sound which is common for all observers.

¨ This shift in frequency (or wavelength) due to the motion of the wave source and/or observer is called the Doppler effect. 15.7 Sound waves from a moving source / Demo

¨ The observed frequency due to the Doppler effect when a source with a frequency � approaches an observer is given by

� � = 1 − �⁄�

� ¨ If the source recedes,

� � = � 1 + �⁄�

¨ Demo: siren on a string Quiz: 15.7-3

¨ A siren emits a sound wave with frequency �. The graph shows the frequency you hear as you stand at rest. Which of the following could be the correct description of the siren’s motion? A. It is stationary at your right side for 2 s, switches to your left quickly, and is again stationary at your left side. B. It moves toward you for 2 s, then reverses direction at t = 2 s. C. It moves away from you for 2 s, then reverses direction at t = 2 s. D. It is circling above your head clockwise for 2 s, then reverses direction at t = 2 s. Quiz: 15.7-3 answer

¨ It moves away from you for 2 s, then reverses direction at t = 2 s. Doppler shift to lower Doppler shift to higher �s frequency means it’s ¨ If the source approaches, �+ = frequency means it’s 1−�s⁄� receding. approaching. ¨ If the source recedes, � = ⁄ Example 15.7-1

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¨ You are standing by a road, and a police car passes by. The frequency of a police siren is 550 Hz as the police car approaches you, and 450 Hz after it passes you and is receding. If the speed of sound is 343 m/s, how fast is the police car traveling? Quiz: 15.7-4

¨ A stationary sound source starts emitting a wave in air when observer Andy is stationary with respect to the source. Then Andy starts moving toward the source. Which of the following quantities of the sound wave change to Andy as he starts moving? Choose all that apply. A. Wavelength B. Frequency C. Speed Quiz: 15.7-4 answer

¨ Speed and Frequency ¨ The frequency of a source in air is � = , so the wavelength established in air is � = . ¨ The wavelength does not change just because he moves, just like the length of bench or any other object does not change just because he moves.

¨ The speed of sound relative to Andy is � = � + �. ¨ Andy observes the frequency of � = = = = 1 + �. ⁄

� 15.7 A stationary source and a moving observer

¨ When an observer is moving relative to the medium, they observe a shift in frequency.

¨ When observer is approaching, � � = 1 + � �

¨ When receding,

� � � = 1 − � � 15.7 The Doppler effect for light waves

¨ The Doppler shift is observed in electromagnetic waves as well.

¨ Since electromagnetic waves do not need medium to propagate, only the relative motion of the source and the observer determines the Doppler shift.

¨ The light you detect from a source moving away from you is red shifted to longer .

¨ The light you detect from a source moving toward you is blue shifted to shorter wavelengths. Quiz: 15.7-5

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¨ Suppose a moth is approaching a . The bat emits a sound wave to detect the motion of the moth. The sound reflects off the moth and travels back to the bat (echo). Compare the of the sound detected at the moth �, of the echo detected by the bat �, and of the source � emitted by the bat, smallest first. Quiz: 15.7-5 answer

¨ � < � < � ¨ Since the moth is moving toward the bat, the sound detected at the moth has a higher frequency due to the Doppler effect.

¨ When the moth reflects off the sound, it becomes a moving source, so the bat (the detector) is detects the echo that is further Doppler- shifted higher. 15.7 Frequency shift on reflection from a moving object

¨ The frequency shift of a wave that is reflected from a moving object is given by

� ∆� = ±2� � Applications of the Doppler effect

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¨ The Doppler effect has many practical applications: weather , speed radar, medical diagnostics, astronomical measurements.

¨ A Doppler can detect not only structure but also motion. Example: 15.7-2

¨ A Doppler ultrasound is used to measure the motion of blood in a patient’s artery. The probe has a frequency of 5.0 MHz, and the maximum frequency shift on reflection is 400 Hz. What is the maximum speed of the blood in the artery?