A pipe open at both ends has a fundamental frequency of 120 Hz.If one end of the pipe is then closed,what is the fundamental frequency of this pipe with one end closed?
A)40 Hz
B)60 Hz
C)80 Hz
D)240 Hz
E)480 Hz

Question

Quizplus · Accepted Answer

When one end of a pipe is closed, the pipe effectively becomes a closed-end resonator. The fundamental frequency of a closed-end resonator is given by f1 = v/4L, where v is the speed of sound and L is the length of the resonator. When one end of the pipe is closed, the effective length of the resonator is half the original length. Therefore, the fundamental frequency of the pipe with one end closed is f1' = v/2L. Since the original fundamental frequency was 120 Hz, we can write this as: f1/f1' = (v/4L)/(v/2L) = 1/2. Solving for f1', we get: f1' = f1/2 = 60 Hz. Therefore, the answer is B.

A Pipe Open at Both Ends Has a Fundamental Frequency