A pipe of 30 cm long open at both the ends produces harmonics. Which harmonic mode of pipe resonates at 1.1 kHz source?  (Take, speed of sound in air = 330 ms^-1)

According to the mode of vibration of air column in an open organ pipe,

First mode of vibration,  $v_1=\frac{v}{2l}$             …(i)

where, v₁ = frequency of vibration,
v = speed of sound and 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,   $v_n=1.1\mathrm{kHz}=1100\mathrm{Hz},v=330{\mathrm{ms}}^{-1}\text{ and }$

l = 30 cm = 0.30 m

Substituting these values in Eq. (ii), we get

$1100=n\times \left(\frac{330}{2\times 0.30}\right)$

$\Rightarrow n=\frac{1100\times 2\times 0.30}{330}\Rightarrow n=\frac{660}{330}=2$

So, second harmonic mode of pipe resonates.