In an open organ pipe $v_{3}$ and $v_{6}$ are $3^{ ext{rd~}}$ and $6^{ ext{th~}}$ harmonic frequen

Question

In an open organ pipe $v_{3}$ and $v_{6}$ are $3^{\text{rd~}}$ and $6^{\text{th~}}$ harmonic frequencies, respectively.

If $v_{6} - v_{3} = 2200\text{ }Hz$ then length of the pipe is

$\_\_\_\_$ mm.

(Take velocity of sound in air is $330\text{ }m/s$.)

Accepted Answer

$f = n\left( \frac{V_{0}}{2L} ight)$$${\frac{6{	ext{ }V}_{0}}{2	ext{ }L} - \frac{3{	ext{ }V}_{0}}{2	ext{ }L} = 2200 }{\frac{3{	ext{ }V}_{0}}{2	ext{ }L} = 2200 }{\frac{3 	imes 330}{2 	imes L} = 2200 }{L = \frac{3 	imes 330}{2 	imes 2200} }{L = 0.225	ext{ }m }{L = 225	ext{ }mm }$$

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