Standing sound waves: The lowest-pitch tone to resonate in a pipe of length L that is open at both ends is 200 Hz. Which one of the following frequencies will NOT resonate in the same pipe?
A) 400 Hz
B) 600 Hz
C) 800 Hz
D) 900 Hz
E) 1000 Hz

Question

Quizplus · Accepted Answer

The resonant frequencies of a pipe that is open at both ends are given by f = n(v/2L), where v is the speed of sound in air, L is the length of the pipe, and n is a positive integer corresponding to the harmonic number. The fundamental frequency, or first harmonic, is when n = 1. So, for a pipe of length L, the fundamental frequency is f1 = v/2L. In this case, f1 = 200 Hz. The second harmonic, or first overtone, occurs when n = 2 and has a frequency of f2 = 2f1 = 400 Hz. The third harmonic, or second overtone, occurs when n = 3 and has a frequency of f3 = 3f1 = 600 Hz. The fourth harmonic, or third overtone, occurs when n = 4 and has a frequency of f4 = 4f1 = 800 Hz. The fifth harmonic, or fourth overtone, occurs when n = 5 and has a frequency of f5 = 5f1 = 1000 Hz. Therefore, all of the given choices are possible frequencies for resonance in the same pipe except for the frequency of 900 Hz, which does not correspond to any of the resonant frequencies for a pipe of length L.

Standing Sound Waves: the Lowest-Pitch Tone to Resonate in a Pipe