Question

The pattern of displacement nodes N and antinodes A in a pipe is NANANANANA when the standing-wave frequency is 1710 Hz

. The pipe contains air at 20∘C
. The speed of sound in air is 344 m/s
What is the fundamental frequency?

Answer 1

The fundamental frequency of the pipe is 11.01 Hz.

Step-by-step explanation:

The fundamental frequency of a standing wave in a pipe can be determined using the formula f = v / λ, where f is the frequency, v is the speed of sound, and λ is the wavelength. In this case, the pattern of displacement nodes (N) and antinodes (A) is NANANANANA, which corresponds to one-fourth of a wavelength. Since there are 10 nodes and antinodes, the total number of segments is 10 + 1 = 11.

Therefore, the wavelength can be calculated by dividing the speed of sound by 11, 344 / 11 = 31.27 m.

Since the fundamental frequency corresponds to one complete wavelength, the length of the pipe can be found by dividing the wavelength by 4, 31.27 / 4 = 7.82 m.

So, the fundamental frequency of the pipe is f = 344 / 31.27 = 11.01 Hz.