Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Topics: • The Principle of Superposition • Standing Waves • Transverse Standing Waves • Standing Sound Waves and Musical
Acoustics • Interference in One Dimension • Interference in Two and Three Dimensions • Beats
Chapter 16. Superposition & Standing Waves
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Reading Quiz 1. When two waves overlap, the displacement of the medium is the sum
of the displacements of the two individual waves. This is the principle of __________.
A. constructive interference B. destructive interference C. standing waves D. superposition
Slide 16-5
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Answer 1. When two waves overlap, the displacement of the medium is the sum
of the displacements of the two individual waves. This is the principle of __________.
A. constructive interference B. destructive interference C. standing waves D. superposition
Slide 16-6
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Reading Quiz 2. A point on a standing wave that is always stationary is a _________.
A. maximum B. minimum C. node D. antinode
Slide 16-7
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Answer 2. A point on a standing wave that is always stationary is a _________.
A. maximum B. minumum C. node D. antinode
Slide 16-8
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Reading Quiz 3. You can decrease the frequency of a standing wave on a string by:
A. making the string longer. B. using a thicker string. C. decreasing the tension. D. all of the above.
Slide 16-9
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Answer 3. You can decrease the frequency of a standing wave on a string by:
A. making the string longer. B. using a thicker string. C. decreasing the tension. D. all of the above.
Slide 16-10
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Standing Wave Modes
Slide 16-15
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There are three things to note about the normal modes of a string. 1. m is the number of antinodes on the standing wave, not
the number of nodes. You can tell a string’s mode of oscillation by counting the number of antinodes.
2. The fundamental mode, with m = 1, has λ1 = 2L, not λ1 = L. Only half of a wavelength is contained between the boundaries, a direct consequence of the fact that the spacing between nodes is λ/2.
3. The frequencies of the normal modes form a series: f1, 2f1, 3f1, …The fundamental frequency f1 can be found as the difference between the frequencies of any two adjacent modes. That is, f1 = Δf = fm+1 – fm.
Standing Waves on a String
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Standing Sound Waves
Slide 16-17
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EXAMPLE: The length of an organ pipe
QUESTION:
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE: The length of an organ pipe
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE: The length of an organ pipe
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
EXAMPLE: The length of an organ pipe
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A standing wave on a string vibrates as shown at the top. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. Which standing wave pattern is produced?
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
A standing wave on a string vibrates as shown at the top. Suppose the tension is quadrupled while the frequency and the length of the string are held constant. Which standing wave pattern is produced?
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
An open-open tube of air supports standing waves at frequencies of 300 Hz and 400 Hz, and at no frequencies between these two. The second harmonic of this tube has frequency A. 800 Hz. B. 200 Hz. C. 600 Hz. D. 400 Hz. E. 100 Hz.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
An open-open tube of air supports standing waves at frequencies of 300 Hz and 400 Hz, and at no frequencies between these two. The second harmonic of this tube has frequency
A. 800 Hz. B. 200 Hz. C. 600 Hz. D. 400 Hz. E. 100 Hz.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Interference in One Dimension The pattern resulting from the superposition of two waves is often called interference. In this section we will look at the interference of two waves traveling in the same direction.
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Two speakers are emitting identical sound waves with a wavelength of 4.0 m. The speakers are 8.0 m apart, directed toward each other, as in the diagram below.
Checking Understanding: Interference Along a Line
At each of the noted points in the above diagram, is the interference
A. constructive? B. destructive? C. something in between?
Slide 16-20
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Two speakers are emitting identical sound waves with a wavelength of 4.0 m. The speakers are 8.0 m apart, directed toward each other, as in the diagram below.
Answer
Slide 16-21
At each of the noted points in the above diagram, is the interference
A. constructive? (a), (c), (e) B. destructive? (b), (d) C. something in between?
