The first overtone frequency of a closed organ pipe P 1 is equal to the fundamental frequency of an open organ pipe P 2 . If the length of the pipe P 1 is 30 cm, what will be the length of P 2 ?

Question

Philoid · Accepted Answer

Given:
Length of closed organ pipe L₁ = 30 cm
Length of open organ pipe L₂ =?

Let and be the frequencies of the closed and open organ pipes, respectively.
The first overtone frequency of a closed organ pipe P₁ is given by

Where v is the speed of sound in air.

On substituting the respective values, we get:

Fundamental frequency of an open organ pipe is given by:

As per the question,

∴ the length of the pipe P₂ will be 20 cm.

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

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