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Unformatted text preview: Physics 1112 Spring 2008 PS #1 Solutions Page 1 of 9 Physics 1112 Problem Set #1 Solutions Problem 1: What region of the spectrum best corresponds to light with a wavelength of. . . (a) the length of a football field? (b) the width of your pinky finger? (c) the thickness of a strand of hair? (d) the size of a virus? (e) the diameter of a hydrogen atom? (f) the size of a proton? (a) A football field is approximately 100 m long, which is clearly in the radio region. (b) A pinky finger is about 1 cm wide. This is definitely in the microwave region. (c) How thick is a strand of hair? If you pluck a hair and hold it up to a ruler, you ought to be able to see that hair is considerably thinner than 1 mm, so a good guess for the thickness might be 0 . 1 mm (this number, also written as 100 μ m or 100 microns, is actually just about right). This thickness is in the far infrared region of the spectrum. (d) The size of a virus can be found in the appendix of “typical values” in the back of your textbook. There you would see that a virus is anywhere from 20 nm to 300 nm in size, which places virus sizes in the ultraviolet range of wavelengths. (e) The diameter of a hydrogen atom is also in the back of your textbook. There it says that the diameter is about 10 − 10 m, which corresponds to a wavelength typical of X-rays. (f) The very first chapter of your textbook lists some typical sizes of objects; it says that a proton is 2 × 10 − 15 m in diameter. A wavelength this small is well into the gamma-ray region of the spectrum. Problem 2: There is a lag of 70 . min when NASA and the European Space Agency radio commands to the Cassini space probe in orbit around Saturn. How far away from Earth is Saturn? The radio waves travel at the speed of light c , just like any other kind of light (visible or not). Since the radio signals travel at a constant speed, d = ct = (3 . 00 × 10 8 m/s)(70 . 0 min) = (3 . 00 × 10 8 m/s)(70 . 0 min) 60 s 1 min = 1 . 26 × 10 12 m . Physics 1112 Spring 2008 PS #1 Solutions Page 2 of 9 Problem 3: (a) Find the wavelength for a typical AM radio wave with a frequency of 970 kHz. (b) Find the wavelength for a typical FM radio wave with a frequency of 98 . 5 MHz. In both parts of this problem, we use the fact that the product of wavelength and frequency is equal to the wave speed for any periodic wave. (a) Using the numbers given, and remembering that units of Hz are equivalent to 1/s, λ = c f = 3 . 00 × 10 8 m/s 970 × 10 3 Hz = 309 m . (b) For these numbers, λ = c f = 3 . 00 × 10 8 m/s 98 . 5 × 10 6 Hz = 3 . 05 m . Problem 4: You’re caught running a red light on Hwy 316. Attempting to impress the skeptical patrol officer with your physics knowledge, you claim that you were traveling so fast that the red light ( λ = 687 nm) actually appeared yellow ( λ = 583 nm) to you. (a) How fast would you have been traveling (in mi/hr) had that been the case? (b) If you had been traveling that fast and the light actually was yellow, what color would it have seemed to you?yellow, what color would it have seemed to you?...
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- Spring '08
- Light, Solutions Page