JEE Main 2026 — Jan 24, Shift 2 — Physics solution

JEE Main2026Jan 24, Shift 2Physics

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 ______.

Solution

Fifth harmonic of a closed pipe: $f_{5, closed} = \frac{5 v}{4 L _{c}}$ (odd harmonics only).

First harmonic (fundamental) of open pipe: $f_{1, open} = \frac{v}{2 L _{o}}$ .

Setting them equal: $\frac{5 v}{4 L _{c}} = \frac{v}{2 L _{o}} \Rightarrow \frac{L _{c}}{L _{o}} = \frac{5}{2}$ .

Comparing with $L_{c} / L_{o} = 5/ x$ , we get $x = 2$ .

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