In an open organ pipe and are 3rd and 6th harmonic frequencies, respectively. If the length of the pipe is _______ mm. (Take velocity of sound in air is

Question

In an open organ pipe $v_{3}$ and $v_{6}$ are 3rd and 6th harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200 Hz,$ the length of the pipe is _______ mm.

(Take velocity of sound in air is 330 m/s) [2026]

Smart Achievers · Accepted Answer

(4)

$f = n (\frac{V_{0}}{2 L})$

$\frac{6 V_{0}}{2 L} - \frac{3 V_{0}}{2 L} = 2200$

$\frac{3 V_{0}}{2 L} = 2200$

$\frac{3 \times 330}{2 \times L} = 2200$

$L = \frac{3 \times 330}{2 \times 2200}$

$L = 0.225 m$

$L = 225 mm$

Solution

Q.
In an open organ pipe $v_{3}$ and $v_{6}$ are 3rd and 6th harmonic frequencies, respectively. If $v_{6} - v_{3} = 2200 Hz,$ the length of the pipe is _______ mm.

(Take velocity of sound in air is 330 m/s) [2026]

1 200

2 250

3 275

4 225

Ans.
(4)

$f = n (\frac{V_{0}}{2 L})$

$\frac{6 V_{0}}{2 L} - \frac{3 V_{0}}{2 L} = 2200$

$\frac{3 V_{0}}{2 L} = 2200$

$\frac{3 \times 330}{2 \times L} = 2200$

$L = \frac{3 \times 330}{2 \times 2200}$

$L = 0.225 m$

$L = 225 mm$

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