You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length $$l$$ and diameter $$\displaystyle\frac{l}{10}$$. You have stretched a string of mass per unit length $$\mu$$ across the open end of the tube. The other end of the tube is closed. To produce the musical effect you are looking for, you want the frequency of the third harmonic standing wave on the string to be same as the fundamental frequency for sound waves in the air column in tube. Velocity of sound in the air column is $$v$$.

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