Question

Consider a pipe with a length of (A+32.5) cm. If the temperature of the air is (12.5+B) ^oC and the pipe is closed in one end and open in the other, what is the frequency of the third harmonic for the pipe? Post your answer in hertz (Hz) and with 3 significant figures.

A= 10

B=0

Answer 1

L = Pipe Length = A+32.5 cm = 10 + 32.5 = 42.5 cm = 0.425m
T = Temperature = 12.5 ^oC

To calculate for the speed of sound at any positive temperature use the formula v = 331m/s + 0.6m/s/C * T where T is the increase in temperature from 0 degrees Celsius. If the temperature is 12.5 degrees Celsius then v = (331 m/s + 7.5 m/s)

V_sound = 338.5 m/s.

Third harmonic frequency = 3 f₁ = 3 * V_sound / 4 L , where L is the length of the pipe

Required frequency = 3 * 338.5 / 4* (0.425) = 597.353 Hz