Question

The velocity of sound in air is $333\text{m/s}$. In order to produce the second overtone of frequency $999\text{Hz}$ in it, the length of the open organ pipe will be :

• A. $0.5\text{m}$
• B. $1\text{m}$
• C. $1.5\text{m}$
• D. $0.25\text{m}$

Answer 1

The correct option is A $0.5\text{m}$

In an open organ pipe all the harmonics are present.
Therefore the frequency of second overtone or third harmonic is,
$f_3=\frac{3v}{2L}$
$\Rightarrow 999=\frac{3\times 333}{2\times L}\Rightarrow L=\frac{1}{2}\text{m}=0.5\text{m}$