Question

A tube of certain diameter '$d$' and of length $48cm$ is open at both ends. Its fundamental frequency of resonance is found to be $320Hz$ and the speed of sound in air is $320m/s$. Estimate the diameter of the tube. If one end of the tube is closed then, calculate the lowest frequency of resonance for the tube.

Answer 1

for open organ pipe

Leff $=L+1.2r$

$=L+0.6d$

$v_0=\frac{v}{Leff}$

$\Rightarrow 2Leff=1m$

$\Rightarrow Leff=50cm$

$\Rightarrow 0.6d=2cm$

$\Rightarrow d-2/0.6=3.33cm$

Now, one end is closed

$Leff=L+0.3d$

$=48+1=49cm$

$v_0=\frac{v}{4Leff}=\frac{320}{(4\times 49)\times {10}^{-2}}$

$=169$