Question

Velocity of sound in air is $320\text{m/s}$. A pipe closed at one end has a length of $1\text{m}$, neglecting end corrections. Find the frequency(s) for which the air column in the pipe can resonate.

• A. $80\text{Hz}$
• B. $240\text{Hz}$
• C. $500\text{Hz}$
• D. $400\text{Hz}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $80\text{Hz}$
B $240\text{Hz}$
D $400\text{Hz}$

Given ,
Length of pipe, $l=1\text{m}$
Speed of sound in air $v=320\text{m/s}$

Modes of vibration of air column in closed organ pipe are given by
$f_n=\frac{(2n-1)v}{4l}\text{where}n=1,2,3,\mathrm{4....}$

[For a closed organ pipe, only odd harmonics are present]

For $n=1,f_1=\frac{320}{4}=80\text{Hz}$
$n=2,f_2=\frac{3\times 320}{4}=240\text{Hz}$
$n=3,f_3=\frac{5\times 320}{4}=400\text{Hz}$
$n=4,f_4=\frac{7\times 320}{4}=560\text{Hz}$

Among the give options, options (a), (b) and (d) are the only modes of vibrations matching with that of a closed organ pipe.