Question

Find the frequency of the fifth overtone of an air column vibrating in a pipe closed at one end. Length of pipe is $42.10$ cm long and speed of sound in air at room temperature is $350$ m/s.

Answer 1

$l=42.10cm$

$=0.4210m$

$v=350m/s$

$d=3.5cm$

$=3.5\times {10}^{-2}m/s$

$=0.035m$

Fundamental frequency in air column closed at one end is given by

$n=\frac{V}{4L}$

$N=\frac{350}{4}\times 0.4315$

$N=\frac{350}{4}\times 0.4315$

$N=202.78Hz$

Pth overtone is given by $np=(2p+1)n$

Frequency of fifth overtone is

$N5=(2\times 5+1)n$

N5=11n

$=11x202.78$

$=2230.59Hz$

∴ the frequency of fifth overtone of an air column vibrating in a pipe closed at one end is $2230.59Hz$