The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe which is L meter long. The length of the open pipe will be

Question

Aicharya · Accepted Answer

Let the length of open organ pipe be $L'$.

Frequency of second overtone of open organ pipe is given as, $f_{1} = \frac{3 v}{2 L'}$ , where $v$ is speed of sound in air.

Frequency of first overtone of closed pipe is given as, $f_{2} = \frac{3 v}{4 L}$ .

According to question, $f_{1} = f_{2}$

$\frac{3 v}{2 L'} = \frac{3 v}{4 L} \Rightarrow L' = 2 L$ .

Hence, length of open organ pipe must be twice the length of closed organ pipe.

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe…

Solution