Chapter 16. Superposition & Standing Waves
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1 Chapter 16. Superposition & Standing Waves 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
2 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
3 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
4 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
5 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
6 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
7 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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9 Standing Wave Modes Slide 16-15
10 Standing Waves on a String 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 λ 1 = 2L, not λ 1 = 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: f 1, 2f 1, 3f 1, The fundamental frequency f 1 can be found as the difference between the frequencies of any two adjacent modes. That is, f 1 = Δf = f m+1 f m.
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14 Standing Sound Waves Slide 16-17
15 EXAMPLE: The length of an organ pipe QUESTION:
16 EXAMPLE: The length of an organ pipe
17 EXAMPLE: The length of an organ pipe
18 EXAMPLE: The length of an organ pipe
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20 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?
21 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?
22 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.
23 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.
24 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.
25 Checking Understanding: Interference Along a Line 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. At each of the noted points in the above diagram, is the interference A. constructive? B. destructive? C. something in between? Slide 16-20
26 Answer 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. 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? Slide 16-21
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