Question

An open organ pipe has fundamental frequency $300Hz$. The first overtone of the open organ pipe is the same as the first overtone of a closed organ pipe. The length (in $cm$) of the closed organ pipe is (Round off the answer to nearest integer) $(v_{sound}=330m/s)$.

Answer 1

Step 1: Find the frequency of first overtone in closed organ pipe.

Given: An open organ pipe has fundamental frequency $n=300Hz$.

Velocity of sound is, $v_{sound}=330m/s$

For open organ pipe,
$n=\frac{v}{2l_1}=300Hz$

For first overtone of open organ pipe,
$\Rightarrow n_0=2\left(\frac{v}{2l_1}\right)=2\times 300$
$\Rightarrow n_0=600Hz$

Step 2: Find the length of the closed organ pipe.

For closed organ pipe,
$\Rightarrow n=\frac{v}{4l_2}$

For first overtone of closed organ pipe is,
$\Rightarrow 3\left(\frac{v}{4l_2}\right)=600Hz$
$\Rightarrow l_2=\frac{3v}{4\times 600}$
$\Rightarrow l_2=\frac{v}{800}$

Velocity is,$v_{sound}=330m/s$
$l_2=\frac{330}{800}=0.41m$

Final Answer: The length of the closed organ pipe is $0.41m$