JEE Main 2026 — Jan 22, Shift 2 — Physics solution

JEE Main2026Jan 22, Shift 2Physics

In an open organ pipe $ν_{3}$ and $ν_{6}$ are 3 $^{r d}$ and 6 $^{t h}$ harmonic frequencies, respectively. If $ν_{6} - ν_{3} = 2200$ Hz then length of the pipe is _____ mm.

(Take velocity of sound in air as 330 m/s.)

A
275
B
225
C
200
D
250

Solution

For an open organ pipe, the $n^{t h}$ harmonic has frequency $ν_{n} = \frac{n v}{2 L}$ .

So $ν_{6} - ν_{3} = \frac{6 v}{2 L} - \frac{3 v}{2 L} = \frac{3 v}{2 L} = 2200$ Hz.

$L = \frac{3 v}{2 \times 2200} = \frac{3 \times 330}{4400} = 0.225$ m $= 225$ mm.

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