Physics Solution Manual for 1100 and 2101

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Unformatted text preview: s the two types of waves. 2. (a) As one domino topples against the next one in line, it is moving partly perpendicular and partly parallel to the direction along which the disturbance propagates. 3. (d) The amplitude specifies the maximum excursion of the spot from the spot’s undisturbed position, and the spot moves through this distance four times during each cycle. For instance, in one cycle starting from its undisturbed position, the spot moves upward a distance A, downward a distance A (returning to its undisturbed position), downward again a distance A, and finally upward again a distance A (returning to its undisturbed position). 4. (d) According to Equation 16.1, the speed v of the wave is related to the wavelength λ and the frequency f by v = f λ . The speed depends only on the properties of the string (tension, mass, and length) and remains constant as the frequency is doubled. According to Equation 16.1, then, the wavelength must be cut in half. 5. 0.80 m 6. (b) The amplitude specifies the maximum excursion of a particle from its undisturbed position and has nothing to do with the wave speed. The amplitude does affect the speed of the simple harmonic motion, however. Equation 10.8 indicates that vmax is proportional to the amplitude. 7. (c) As discussed in Section 16.3, the speed of the wave is greater when the tension in the rope is greater, which it is in the upper portion of the rope. The rope has a mass m and, hence, a weight. The upper portion of the rope has a greater tension than does the lower portion, because the upper portion supports the weight of a greater length of rope hanging below. 8. (e) According to Equation 16.2, the speed is proportional to the square root of the tension. Since the tension in string 1 is three times that in string 2, the speed in string 1 is 3 = 1.73 times the speed in string 2. 9. 0.0039 kg/m 10. 161 m/s 11. (e) Condensations are regions where the air pressure is increased above the normal pressure, and rarefactions are regions where the air pressure is decreased below the normal pressure. When the amplitude decreases to zero, the pressure of the air is no longer being increased Chapter 16 Answers to Focus on Concepts Questions 833 above or being decreased below the normal air pressure. Therefore, there are no longer any condensations or rarefactions. 12. (b) Sound travels faster in liquids than in gases. The greater speed in water ensures that the echo will return more quickly in water than in air. 13. (d) The frequency of the sound is determined by the vibrating diaphragm of the horn. The sound wave travels through the air and contacts the surface of the water, where it causes the water molecules to vibrate at the same frequency as the molecules in the air. However, the speed of sound in air is smaller than in air. According to Equation 16.1, the wavelength is proportional to the speed, when the frequency is constant. As a result, the wavelength is smaller in the air than in the water. 14. (a) According to Equation 16.5, the speed of sound in an ideal gas is directly proportional to the square root of the Kelvin temperature. This means that the speed at the higher temperature of 30.0 + 273.15 = 303 K is greater than the speed at the lower temperature of 303 K 15.0 + 273.15 = 288 K by a factor of . Thus, the desired speed is (275 m/s) 288 K 303 K . 288 K 15. 9.0 W 16. 4.77 dB 17. 0.45 18. (c) The Doppler effect causes the observed frequency to be shifted toward higher values when the source moves toward a stationary observer and when the observer moves toward a stationary source. The shift to higher observed frequencies is even greater when the source and the observer move toward each other, as they do here. In Equation 16.15 the plus sign applies in the numerator and the minus sign in the denominator. 19. (d) In order for the Doppler effect to be large, the speed vs of the source and/or the speed vo of the observer must be appreciable fractions of the speed v of sound. The Doppler effect depends on vs/v or vo/v or on both of these ratios (See Equations 16.11 – 16.15.) For given values of vs and vo, these ratios decrease, and the Doppler effect decreases as the speed of sound increases. The speed of sound in air (assumed to be an ideal gas) increases with temperature, according to Equation 16.5. Therefore, the Doppler effect decreases with increasing temperature, no matter if the source moves, the observer moves, or both move. 20. 992 Hz 834 WAVES AND SOUND CHAPTER 16 WAVES AND SOUND PROBLEMS ______________________________________________________________________________ 1. SSM REASONING Since light behaves as a wave, its speed v, frequency f, and wavelength λ are related to according to v = f λ (Equation 16.1). We can solve this equation for the frequency in terms of the speed and the wavelength. SOLUTION Solving Equation 16.1 for the frequency, we find that f= 2. v λ = 3.00 ×108 m/s = 5.50 ×1014 Hz −7 5.45 ×10 m REASONING We can think of the rumble strips as a wave carved into the surface of the road. The wave is stationary relative to the road, but it...
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