Question

A pipe $30cm$ long, is open at both ends. Which harmonic mode of the pipe resonates a $1.1kHz$ source? (Speed of sound in air = $330m{s}^{-1})$

• A. Fifth harmonic
• B. second harmonic
• C. Third harmonic
• D. Fourth harmonic

Answer 1

Answer: (B)

According to the modes of vibration of air column in open organ pipe,
First mode of vibration
$v_1=\frac{V}{2l}\dots (i)$
where $v_1=$ frequency of vibration
v= speed of sound
l= length of organ pipe
The frequency of nth mode of vibration
$v_n=n\times v_1$
$=n\times \left(\frac{V}{2l}\right)$
Given, $v_n=1.1kHz=1100Hz$
$V=330m{s}^{-1}$
$l=30cm=0.30m$
$1100=n\times \left(\frac{330}{2\times 0.30}\right)$
$n=\frac{1100\times 2\times 0.30}{330}$
$n=\frac{660}{330}=2$
So, second harmonic mode of pipe resonates.