Question: A New Musical Instrument. You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L

A New Musical Instrument. You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length L and diameter L/10. You have stretched a string of mass per unit length I' across the open end of the tube. The other end of the tube is closed. To produce the musical effect you're looking for. You want the frequency of the third-harmonic standing wave on the string to be the same as the fundamental frequency for sound waves in the air column in the tube. The speed of sound waves in this air column is v 8.
(a) What must be the tension of the string to produce the desired effect?
(b) What happens to the sound produced by the instrument if the tension is changed to twice the value calculated in part (a)?
(c) For the tension calculated in part (a), what other harmonics of the string, if any, are in resonance with standing waves in the air column?

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IDENTIFY The harmonics of the string are f nf n where is the length of the string The tube is a stop... View full answer

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