Question

The frequency of an open pipe is $300Hz$. The first overtone of this pipe is the same as the second overtone of a closed pipe. The length of the closed organ pipe is

• A. $11cm$
• B. $21cm$
• C. $69cm$
• D. $84cm$

Answer 1

Answer: (C)

$69cm$

Velocity of sound in air $v=330m/s$

Let $L^{\prime }$ and $L$ be the lengths of closed and open pipe respectively.

Fundamental frequency of an open pipe ${\nu }_1=300Hz$

Frequency of 1st overtone in an open pipe ${\nu }_2=2{\nu }_1=600Hz$

Frequency of second overtone in a closed pipe ${\nu }_3^{\prime }=\frac{5v}{4L^{\prime }}$

But ${\nu }_2={\nu }_3^{\prime }⟹600=\frac{5\times 330}{4L^{\prime }}$

$⟹L^{\prime }=0.6875m=68.75cm$