Question

Two open tubes both have actual length

1 m, but their diameters are D1 = 1 cm and D2 = 10 cm. Allowing for end corrections,

what are their fundamental frequencies? Don't forget that the tubes are open on both

ends.

Answer 1

The wavelength of the fundamental frequency for a completely open pipe is twice the length of the tube: = 2l or l = /2.

Considering end correction the expression for : = 2L + 4C

The equation relating the wavelength of a wave, to the frequency of the wave : v = f

The end correction for open tube = D/2

Speed of sound is 343 m/s

Case 1, D1 = 1 cm = 0.01 m

= 2*1 + 4* (0.01/2) = 2.02 m

Thus f = v / = 343/2.02 = 169.8 Hz

Case 2 D2 = 10 cm = 0.1 m

= 2*1 + 4* (0.1/2) = 2.2 m

Thus f = v / = 343/2.2 = 155.91 Hz