An organ pipe open at both ends has a length of 0.80 m. If the velocity of sound in air is $340 \mathrm {~m} / \mathrm { s }$ what is the frequency of the second harmonic of this pipe?
A)213 Hz
B)425 Hz
C)638 Hz
D)850 Hz

Question

Quizplus · Accepted Answer

An open pipe supports harmonics at multiples of the fundamental frequency. The fundamental frequency $ f_1 $ is given by $ f_1 = \frac{v}{2L} $. For the second harmonic, $ f_2 = 2f_1 = \frac{2v}{2L} = \frac{v}{L} $. Substituting $ v = 340 \, \text{m/s} $ and $ L = 0.80 \, \text{m} $, we get $ f_2 = \frac{340}{0.80} = 425 \, \text{Hz} $.

An Organ Pipe Open at Both Ends Has a Length 340 m/s340 \mathrm {~m} / \mathrm { s }340 m/s

An Organ Pipe Open at Both Ends Has a Length $340 \mathrm {~m} / \mathrm { s }$