Question

The first overtone of an open organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fundamental frequency of the closed organ pipe is 110 Hz. Find the lengths of the pipes. 

Answer 1

Allowed frequencies of an open organ pipe are

Allowed frequencies of a closed organ pipe are

The length of the closed organ pipe = l₂ = 0.75 m

which is the length of the open organ pipe.

Answer 2

Let L₁ and L₂ be the lengths of open and close pipes respectively. The frequency of first overtone of an open organ pipe

= 2v/2L₁ 

The frequency of first overtone of closed organ pipe

= 3v/4L₂ 

Given fundamental frequency of closed organ pipe 

∴ L₂ = 0.75 m

As the beats frequency is 2.2 Hz, so