Sound WavesMedium
Question
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 $5/x$. The value of x is $\_\_\_\_$ .
Options
A.4
B.2
C.1
D.3
Solution
$\ f_{5\text{~closed~}} = f_{1\text{~open~}}$
$${\frac{5v}{4{\text{ }L}_{\text{closed~}}} = \frac{v}{2{\text{ }L}_{\text{open~}}} }{\frac{L_{\text{closed~}}}{L_{\text{open~}}} = \frac{5}{2} }{x = 2}$$
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