The rate of vibration (frequency) of a string under

Chapter 7, Problem 7.5.19

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The rate of vibration (frequency) of a string under constant tension is inversely proportional to the length of the string. (See Explore & Extend 7.5.) a. Write an equation for the vibration rate of a string, f, as a function of its length, L. b. If a 48-inch string vibrates 256 times per second, then how long is a string that vibrates 512 times per second? c. In general, it can be said that if the length of the string increases, the vibration rate will _______. d. If you want the vibration rate of a string to increase, then you must _________ the length of the string. e. Playing a stringed instrument, such as a guitar, dulcimer, banjo, or fiddle, requires placing your finger on a fret, effectively shortening the string. Doubling the vibration produces a note pitched one octave higher, and halving the vibration produces a note pitched one octave lower. If the number of vibrations decreased from 440 to 220 vibrations per second, what happened to the length of the string to cause the change in vibration?