Post on 22-Dec-2015
Dr. Jie Zou PHY 1151G Department of Physics 1
Chapter 14
Waves and Sound (Cont.)
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Outline Standing waves
Standing waves on a string Vibrating columns of air
Sound intensity Doppler effect
Moving observer Moving source
A standing wave A standing wave is one that
oscillates with time, but remains fixed in its location. It is in this sense that the wave is said to be “standing”.
Example: (a) A string tied down at both ends; (b) When plucked in the middle, a
standing wave results-the fundamental mode of oscillation of the string.
1 = 2L (wavelength of the fundamental)
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Standing waves on a string
First harmonic (fundamental) frequency and wavelength: f1 = v/(2L); 1 = 2L
v = (F/)1/2: wave speed on the string; F: tension in the string; : mass per unit length of the string; L: length of the string
Frequency and wavelength of the nth harmonic, with n = 1, 2, 3,…: fn = nf1 = ; n = 1/n = 2L/n
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L
vn2
Node (N)
Antinode (A)
An application – guitar
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Vibrating columns of air Standing waves in a
column of air closed at one end:
f1 = v/(4L); fn = nf1 = , n = 1, 3, 5,
… odd harmonics only n = 1/n = 4L/n v: speed of sound in air L: length of the air
column
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L
vn4
Example An empty soda pop bottle is to be
used as a musical instrument in a band. In order to be tuned properly, the fundamental frequency of the bottle must be 440.0 Hz.
(a) If the bottle is 26.0 cm tall, how high should it be filled with water to produce the desired frequency? Treat the bottle as a pipe that is closed at one end (the surface of the water) and open at the other end. (6.5 cm)
(b) What is the frequency of the next higher harmonic for this bottle? (1320 Hz)
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Sound intensity The loudness of a sound is
determined by its intensity. Definition of intensity: If the
energy E passes through the area A in the time t, the intensity, I, of the wave is I = E/(At). Since the power P = E/t, I = P/A. SI unit: W/m2.
The intensity falls off with the square of the distance: I = P/(4r2). SI unit: W/m2.
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Example: Intensity of sound
Two people relaxing on a deck listen to a songbird sing. One person, only 1.00 m from the bird, hears the sound with an intensity of 2.80 10-6 W/m2 .
What intensity is heard by the second person, who is 4.25 m from the bird? Assume that no reflected sound is heard by either person.
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Doppler effect
Doppler effect: The change in pitch, due to the relative motion between a source of sound and the receiver, is called the Doppler effect. The pitch increases when the
observer and the source are moving closer together.
The pitch decreases when the observer and source are separating.
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Doppler effect for a moving observer
For moving observer: f´= (1 u/v)f f´= frequency to the observer. f = frequency of the source of
the sound. u = speed of the observer. v = speed of the sound. “+”: when the observer
moves toward the source. “-”: when the observer moves
away from the source.
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Doppler effect for a moving source
For moving source: f’ = [1/(1 u/v)] f u = speed of the source. v = speed of the sound. “-”: when the source
moves toward the observer.
“+”: when the source moves away from the observer.
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Example: Doppler effect A train sounds its whistle as it
approaches a tunnel in a cliff. The whistle produces a tone of 650.0 Hz, and the train travels with a speed of 21.2 m/s.
(a) Find the frequency heard by an observer standing near the tunnel entrance.
(b) The sound from the whistle reflects from the cliff back to the engineer in the train. What frequency does the engineer hear?
Dr. Jie Zou PHY 1151G Department of Physics 14
Homework See online homework assignment
on www.masteringphysics.com