Question

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

Answer 1

Correct Answer: 80

An open organ pipe has its fundamental frequency at the first harmonic, given by f_open = v/2L_open, where v is the speed of sound and L_open the length of the pipe.

The first overtone frequency in an open pipe is its second harmonic: f₂ = 2(v/2L_open) = v/L_open.

A closed organ pipe has its fundamental frequency at the first harmonic as f_closed = v/4L_closed.

We're told f_2,open = f_closed. Hence, v/L_open = v/4L_closed.

Simplifying gives: L_open = 4L_closed.

Given L_closed = 20 cm, we calculate: L_open = 4 × 20 = 80 cm.

Therefore, the length of the open organ pipe is 80 cm, which satisfies the range 80,80.