Question

The fundamental frequency of a closed organ pipe is same as the first overtone frequency of an open pipe. The length of open pipe is $20cm$. The length of closed pipe is

• A. $25cm$
• B. $12.5cm$
• C. $13.33cm$
• D. $200cm$

Answer 1

The correct option is C $13.33cm$

Given $:-$

Fundamental Frequency for the Open orange pipe $=\nu /2l^{\prime }$

where$,\nu =$ Frequency and l' is the length of the open orange pipe$.$

Third Harmonic of the orange pipe $=3\nu /4l$

where$,\nu =$ frequency

and $l$ is the length of the Closed orange pipe $=20cm.$

Now$,$ According to the Question$,$

$3\nu /4l=\nu /2l^{\prime }$

$\Rightarrow 3/(4\times 20)=1/2l^{\prime }$

$\Rightarrow 3/80=1/2l^{\prime }$

$\Rightarrow 2l^{\prime }=80/3$

$\Rightarrow l^{\prime }=40/3$

$\Rightarrow l^{\prime }=13.33cm.$

Hence,

option $\left(C\right)$ is correct answer.