Question

The first overtone frequency of a closed organ pipe P1 is equal to the fundamental frequency of a open organ pipe P2. If the length of the pipe P1 is 30 cm, what will be the length of P2?

Answer 1

The first overtone frequency of a closed organ pipe P1 is equal to the fundamental frequency of a open organ pipe P2. If the length of the pipe P1 is 30 cm, The length of P2 is 20 cm.

Explanation:  

Given data,  

As per the questions

A closed organ pipe P1 has the first overtone frequency equal to the fundamental frequency of an open organ pipe P2.

The P1 pipe is 30 cm long

$P 1=\frac{3 V}{4 l}=3 \times \frac{V}{4} \times 30$

F2 Fundamental free organ pipe frequency $P_{2}=\frac{V}{2 I_{2}}$

Here given $\frac{3 V}{4} \times 30=\frac{V}{2 I_{2}}$

=$20 \mathrm{cm}$

Pipe P2 will be 20 cm long.