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Unformatted text preview: Physics 1240 Homework 10 solutions Brief solutions to homework set #10. Your numbers will be different, but the idea is the same. I’m just using sample numbers here. 1. Decide whether each of the following statements are TTrue, or FFalse. (a) If an ideal string can vibrate in a pure standing wave with fundamental frequency f , then (with no changes in length, tension, or material) it can also be made to vibrate in a pure standing wave with frequency of f/ 2. False. The fundamental is the lowest frequency resonance, because it corresponds to the longest wavelength that “fits” on the string. A lower frequency wave wouldn’t fit. (See more explanation of this point in the answer to question 5, below.) (b) If you decrease the tension in a string, the frequency of its fundamental vibration will get higher. False. Lower tension means lower wave speed along the string (because v is proportional to √ Tension), which means lower frequency (because v = fλ and λ doesn’t change). (c) If you have a standing wave with frequency 5 times the fundamental, there are 5 internal nodes (not counting nodes at the end of the string). False. The 5th mode has 5 antinodes and 4 interior nodes. (d) If an ideal string can vibrate in a pure standing wave with frequency f , then (with no changes in length, tension, or material) it can also be made to vibrate in a pure standing wave with frequency of 3 f . True. The third harmonic has frequency f 3 = 3 f ....
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This note was uploaded on 08/24/2010 for the course PHYS 1240 taught by Professor Holland,murray during the Spring '08 term at Colorado.
 Spring '08
 HOLLAND,MURRAY
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