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  4. For a certain organ pipe, three successive resonance frequencies are observed at 425 Hz , 595 Hz and 765 Hz respectively. If the speed of sound in air is 340 m / s, then the length (in m) of the pipe is?

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Q. For a certain organ pipe, three successive resonance frequencies are observed at $425\, Hz , 595\, Hz$ and $765 \,Hz$ respectively. If the speed of sound in air is $340 \,m / s$, then the length (in $m$) of the pipe is?

Waves

Solution:

The ratio of frequencies is
$425: 595: 765=5: 7: 9$
So clearly as consecutive frequencies are odd multiples of a fundamental frequency $v$ and pipe is a closed pipe closed at both ends.
Hence, $\frac{5 v}{4 L}=425$
$\Rightarrow \frac{5(340)}{4 L} =425$
$L =\frac{5 \times 340}{4 \times 425}=1\, m$