Waves

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80 of 142

Question 80 of 142

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is 5/x5 / x. The value of xx is ____\_\_\_\_.

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Answer: (D) 2

Fifth harmonic of closed organ pipe equals first harmonic of open pipe:
f5 closed=f1 openf_{5\text{ closed}} = f_{1\text{ open}}
5v4Lclosed=v2Lopen\frac{5v}{4L_{\text{closed}}} = \frac{v}{2L_{\text{open}}}
LclosedLopen=52\frac{L_{\text{closed}}}{L_{\text{open}}} = \frac{5}{2}
Since the ratio is 5x\frac{5}{x}, we get x=2x = 2.

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