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 . The value of is _______ . [2026]

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 $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

Smart Achievers · Accepted Answer

(4)

$f_{5 closed} = f_{1 open}$

$\frac{5 v}{4 L_{closed}} = \frac{v}{2 L_{open}}$

$\frac{L_{closed}}{L_{open}} = \frac{5}{2}$

$x = 2$

Solution

Q.
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 $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

1 1

2 3

3 4

4 2

Ans.
(4)

$f_{5 closed} = f_{1 open}$

$\frac{5 v}{4 L_{closed}} = \frac{v}{2 L_{open}}$

$\frac{L_{closed}}{L_{open}} = \frac{5}{2}$

$x = 2$

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Solution

Q. 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 5x. The value of x is _______ . [2026]

1 1

2 3

3 4

4 2

Ans. (4) f5 closed=f1 open 5v4Lclosed=v2Lopen LclosedLopen=52 x=2

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Q.
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 $\frac{5}{x}$ . The value of $x$ is _______ . [2026]

Ans.
(4)

$f_{5 closed} = f_{1 open}$

$\frac{5 v}{4 L_{closed}} = \frac{v}{2 L_{open}}$

$\frac{L_{closed}}{L_{open}} = \frac{5}{2}$

$x = 2$