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Unformatted text preview: CHAPTER 17 THE PRINCIPLE OF LINEAR SUPERPOSITION AND INTERFERENCE PHENOMENA ANSWERS TO FOCUS ON CONCEPTS QUESTIONS ____________________________________________________________________________________________ 1. (d) If we add pulses 1 and 4 as per the principle of linear superposition, the resultant is a straight horizontal line that extends across the entire graph. 2. (a) These two pulses combine to produce a peak that is 4 units high and a valley that is 2 units deep. No other combination gives greater values. 3. (c) The smallest difference in path lengths for destructive interference to occur is one-half a wavelength ( 29 1 2 . As the frequency goes up, the wavelength goes down, so the separation between the cellists decreases. 4. Smallest separation = 1.56 m 5. (b) According to Equation 17.2, the diffraction angle is related to the wavelength and diameter by ( 29 sin 1.22 / D = and is determined by the ratio / D . Here the ratio is 2 / D and is the largest of any of the choices, so it yields the largest diffraction angle. 6. = 30.0 degrees 7. (e) Since the wavelength is directly proportional to the speed of the sound wave (see Section 16.2), the wavelength is greatest in the helium-filled room. The greater the wavelength, the greater the diffraction angle (see Section 17.3). Thus, the greatest diffraction occurs in the helium-filled room. 8. (d) The trombones produce 6 beats every 2 seconds, so the beat frequency is 3 Hz. The second trombone can be producing a sound whose frequency is either 438 Hz - 3 Hz = 435 Hz or 438 Hz + 3 Hz = 441 Hz. 9. Beat frequency = 3.0 Hz 10. (d) According to the discussion in Section 17.5, one loop of a transverse standing wave corresponds to one-half a wavelength. The two loops in the top picture mean that the wavelength of 1.2 m is also the distance L between the walls, so L = 1.2 m. The bottom picture contains three loops in a distance of 1.2 m, so its wavelength is ( 29 2 3 1.2 m 0.8 m. = 133 THE PRINCIPLE OF LINEAR SUPERPOSITION AND INTERFERENCE PHENOMENA 11. (b) The frequency of a standing wave is directly proportional to the speed of the traveling waves that form it (see Equation 17.3). The speed of the waves, on the other hand, depends on the mass m of the string through the relation ( 29 / / v F m L = , so the smaller the mass, the greater is the speed and, hence, the greater the frequency of the standing wave. 12. (c) For a string with a fixed length, tension, and linear density, the frequency increases when the harmonic number n increases from 4 to 5 (see Equation 17.3). According to = v / f (Equation 16.1), the wavelength decreases when the frequency increases. 13. Fundamental frequency = 2.50 10 2 Hz 14. (c) One loop of a longitudinal standing wave corresponds to one-half a wavelength. Since this standing wave has two loops, its wavelength is equal to the length of the tube, or 0.80 m....
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- Fall '11