Question

A standing wave of the fifth harmonic is induced in a stopped pipe of length 1. 5 m. The speed of sound through the air of the pipe is 340 m/s. How many antinodes form in the standing wave pattern?

A) 5

B) 3

C) 7

D) 6

E) 4

Answer 1

To find the number of antinodes in the standing wave pattern, we need to find the wavelength of the fifth harmonic. The fifth harmonic has a frequency of 5 times the fundamental frequency, and the fundamental frequency is equal to the speed of sound divided by the length of the pipe. Thus, the wavelength of the fifth harmonic is the speed of sound divided by 5 times the fundamental frequency, which is equal to 340 m/s / (5 * (340 m/s / 1.5 m)) = 0.3 m.

Since the length of the pipe is 1.5 m, and the wavelength is 0.3 m, there will be 1.5 m / 0.3 m = 5 full wavelengths in the pipe. Since there is an antinode at both ends of the pipe, there will be a total of 5 + 2 = 7 antinodes in the standing wave pattern. Therefore, the correct answer is (C) 7.