Question

The fundamental frequency of a open organ pipe is $300Hz$. The first overtone of this pipe is the same as the first overtone of a closed organ pipe. If the speed of sound be $330m{s}^{-1}$, then the length of the closed organ pipe is

• A. $10cm$
• B. $41.25cm$
• C. $82cm$
• D. $164cm$

Answer 1

The correct option is B $41.25cm$

Fundamental frequency of an open organ pipe is given by ,

$n_1=v/\lambda =v/2l$ ,

where $v=$speed of sound in air ($=330m/s,given$),

$\lambda =$ wavelength ,

$l=$ length of organ pipe ,

$n_1=300Hz$

therefore , $n_1=330/\left(2l\right)$ ,

or $l=330/\left(2n_1\right)=330/(2\times 300)=0.55m$ ,

now given , first overtone of open pipe =first overtone of closed pipe ,

$v/l=3v/4l^{\prime }$ , where $l^{\prime }=$ length of closed pipe ,

or $l^{\prime }=3l/4=3\times 0.55/4=0.4125m=41.25cm$