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77. Il Show that the Doppler frequency f. of a receding source is f_=fo/(1+v₂/v).

77. Il Show that the Doppler frequency f. of a receding source is f_=fo/(1+v₂/v).

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7:22 PM Wed Feb 8 Physics for Scientists and Engineers A Strategic Approach by Randall D. Knight to my toward her from the back of the stage. The dat will de outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 2¹/¹2 = 1.059. With what speed must the bat fly toward the singer? 76. ||| A loudspeaker on a pole is radiating 100 W of sound energy in all CALC directions. You are walking directly toward the speaker at 0.80 m/s. When you are 20 m away, what are (a) the sound intensity level and (b) the rate (dB/s) at which the sound intensity level is increasing? Hint: Use the chain rule and the relationship log₁0x = ln x/ln 10. 77. || Show that the Doppler frequency ƒ of a receding source is f_=fo/(1 + vg/v). 78. I A starship approaches its home planet at a speed of 0.10c. When it is 54 × 106 km away, it uses its green laser beam (λ = 540 nm) to signal its approach. a. How long does the signal take to travel to the home planet? b. At what wavelength is the signal detected on the home planet? 79. Wavelengths of light from a distant galaxy are found to be 0.50% longer than the corresponding wavelengths measured in a terrestrial laboratory. Is the galaxy approaching or receding from the earth? At what speed? IT HOL 10 ●●● 17 Superposition index of refraction changes with distance from the front surface. FIGURE CP16.84 shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increas- es linearly from n₁ at the front surface to n₂ at the rear surface. a. Find an expression for the time light takes to travel through this piece of glass. = b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n₁ 1.50 and n₂ = 1.60. 85. ||| A water wave is a shallow-water wave if the water depth d is less CALC than ≈ λ/10. It is shown in hydrodynamics that the speed of a shal- low-water wave is v = √gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than 10 m. Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.0 m at a distance of 100 m. How long does it take a wave to move the last 100 m to the shore? Assume that the waves are so small that they don't break before reaching the shore. 1₂ 17 Superposition n1 1 0 0 FIGURE CP16.84 L -Distance 70% Done
Transcribed Image Text:7:22 PM Wed Feb 8 Physics for Scientists and Engineers A Strategic Approach by Randall D. Knight to my toward her from the back of the stage. The dat will de outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 2¹/¹2 = 1.059. With what speed must the bat fly toward the singer? 76. ||| A loudspeaker on a pole is radiating 100 W of sound energy in all CALC directions. You are walking directly toward the speaker at 0.80 m/s. When you are 20 m away, what are (a) the sound intensity level and (b) the rate (dB/s) at which the sound intensity level is increasing? Hint: Use the chain rule and the relationship log₁0x = ln x/ln 10. 77. || Show that the Doppler frequency ƒ of a receding source is f_=fo/(1 + vg/v). 78. I A starship approaches its home planet at a speed of 0.10c. When it is 54 × 106 km away, it uses its green laser beam (λ = 540 nm) to signal its approach. a. How long does the signal take to travel to the home planet? b. At what wavelength is the signal detected on the home planet? 79. Wavelengths of light from a distant galaxy are found to be 0.50% longer than the corresponding wavelengths measured in a terrestrial laboratory. Is the galaxy approaching or receding from the earth? At what speed? IT HOL 10 ●●● 17 Superposition index of refraction changes with distance from the front surface. FIGURE CP16.84 shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increas- es linearly from n₁ at the front surface to n₂ at the rear surface. a. Find an expression for the time light takes to travel through this piece of glass. = b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n₁ 1.50 and n₂ = 1.60. 85. ||| A water wave is a shallow-water wave if the water depth d is less CALC than ≈ λ/10. It is shown in hydrodynamics that the speed of a shal- low-water wave is v = √gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than 10 m. Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.0 m at a distance of 100 m. How long does it take a wave to move the last 100 m to the shore? Assume that the waves are so small that they don't break before reaching the shore. 1₂ 17 Superposition n1 1 0 0 FIGURE CP16.84 L -Distance 70% Done
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