H1 Physics 112-1 F 12 Page 1 of 1
Homework #1: Chapter 14
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#1: What distinguishes a wave from an oscillation?
#10: Medical ultrasound uses frequencies on the order of 10 7 Hz, far above the range of the human ear.
In what sense are these waves “sound”?
#15: Why can a boat easily produce a shock wave on the water surface, while only a very high-speed aircraft can produce a sonic boom?
#18: An 88.7MHz FM radio wave propagates at the speed of light. What’s its wavelength?
#26: Analysis of waves in shallow water (depth much less than wavelength) yields the following wave equation:
𝜕
2 𝑦
𝜕𝑥 2
1
= 𝑔ℎ
𝜕
2
𝜕𝑡 𝑦
2
Where h is greater than the water depth and g is the gravitational acceleration. Give and expression for the wave speed.
#31: A rope with 280g of mass per meter is under 550N tension. Find the average power carried by a wave with frequency 3.3Hz and amplitude 6.1cm propagating on the rope.
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#39: What’s the wavelength of the ocean waves in Example 14.5 (Edition 2, page234; Edition 1, page
231) if the calm water you encounter at 33m is the second calm region on your voyage from the center line?
#63: You see an airplane 5.2km straight overhead. Sound from the plane, however, seems to be coming from a point back along the plane’s path at 35° to the vertical. What’s the plane’s speed, assuming an average sound speed of 330m/s?
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#72: Show by differentiation and direct substitution that any function of the form 𝑦 = 𝑓(𝑥 ± 𝑣𝑡) satisfies the wave equation.
#81: You’re a meteorologist specifying a new Doppler radar system that determines the velocity of distant raindrops by reflecting radar signals (which travel at the speed of light) off them and measuring the Doppler shift. You need a system that will measure speeds as low as 2.5 km/h. A vendor offers a
5.0GHz radar that can detect a frequency shift of only 50 Hz. Is that sufficient?