JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Waves & Sound

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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 ____.

(A)4
(B)2✓ Correct
(C)1
(D)3

Answer: (B)

Solution

A closed organ pipe supports only odd harmonics, and its fifth harmonic has frequency

f = \frac{5 v}{4 L _{c}}

. The first harmonic of an open pipe is

f = \frac{v}{2 L _{o}}

. Unison sets these equal:

\frac{5 v}{4 L _{c}} = \frac{v}{2 L _{o}}

, so

\frac{L _{c}}{L _{o}} = \frac{5}{2}

. Comparing with the stated

\frac{5}{x}

, the value of

x

2

JEE Main · 2026 · 24 Jan 2026 · Shift 2 · Single correct option

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