Ch16

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Unformatted text preview: CHAPTER 16 Superposition and Standing Waves 1* True or false: ( a ) The waves from two coherent sources that are radiating in phase interfere constructively everywhere in space. ( b ) Two wave sources that are out of phase by 180 o are incoherent. ( c ) Interference patterns are observed only for coherent sources. ( a ) False ( b ) False ( c ) True 2 Two violinists standing a few feet apart are playing the same notes. Are there places in the room where certain notes are not heard because of destructive interference? Explain. No; the two sources are incoherent and do not give rise to interference. 3 Two rectangular wave pulses are traveling in opposite directions along a string. At t = 0, the two pulses are as shown in Figure 16-27. Sketch the wave functions for t = 1, 2, and 3 s . Chapter 16 Superposition and Standing Waves 4 Repeat Problem 3 for the case in which the pulse on the right is inverted. 5* Two waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelength of 2 cm, and an amplitude of 0.02 m. What is the amplitude of the resultant wave if the original waves differ in phase by ( a ) p /6, and ( b ) p /3? ( a ) A = 2 y 0 cos 1/2 d ( b ) Repeat for d = p /3 A = 4 cos p /12 cm = 3.86 cm A = 4 cos p /6 cm = 3.46 cm 6 What is the phase difference between the two waves of Problem 5 if the amplitude of the resultant wave is 0.02 m, the same as the amplitude of each original wave? Now cos d /2 = 0.5 d = 120 o = 2 p /3 rad 7 Two waves having the same frequency, wavelength, and amplitude are traveling in the same direction. If they differ in phase by p /2 and each has an amplitude of 0.05 m, what is the amplitude of the resultant wave? A = 2 y cos p /4 A = 7.07 cm 8 Two sound sources oscillate in phase with the same amplitude A . They are separated in space by l /3. What is the amplitude of the resultant wave from the two sources at a point that is on the line that passes through the sources but is not between the sources? Use Equs. 16-9 and 16-6 d = 2 p /3; A res = 2 A cos p /3 = A Chapter 16 Superposition and Standing Waves 9* Two sound sources oscillate in phase with a frequency of 100 Hz. At a point 5.00 m from one source and 5.85 m from the other, the amplitude of the sound from each source separately is A. ( a ) What is the phase difference in the sound waves from the two sources at that point? ( b ) What is the amplitude of the resultant wave at that point? ( a ) Find x / l , then use Equ. 16-9 ( b ) Apply Equ. 16-6 l = 3.4 m; x / l = 0.25; d = 90 o A res = 2 A cos 45 o = A 2 10 With a compass, draw circular arcs representing wave crests originating from each of two point sources a distance d = 6 cm apart for l = 1 cm. Connect the intersections corresponding to points of constant path difference, and label the path difference for each line. (see Figure 16-8) The Figure is shown below. Lines of constructive interference are shown for path differences of 0, l , 2 l , and 3...
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