A pipe 0.570 m long and closed at one end is filled with an unknown gas. The third lowest harmonic frequency for the pipe is 780 Hz.

(a) What is the speed of sound in the unknown gas?

(b) What is the fundamental frequency for this pipe when it is filled with the unknown gas?

a. v = 355.68 m / s

b. fₙ = 156 Hz

Explanation:

Given

L = 0.570 m, f = 780 Hz

f = n * v / 4 * L

Solve to u' to find the speed of sound in the unknown gas

v = f * 4 * L / n

v = 780 Hz * 4 * 0.570 m / 5

v = 355.68 m / s

The fundamental frequency for this pipe when it is filled with the unknown gas

fₙ = f / n

fₙ = 780 Hz / 5

fₙ = 156 Hz