The animation below shows a representation of a particular longitudinal standing

Question

The animation below shows a representation of a particular longitudinal standing wave that is set up in a pipe which is closed at one end. A somewhat simpler transverse representation of the standing wave is shown in red, above the pipe. The speed of sound is 340 m/s, and the frequency of the standing wave is 900 Hz. The animation shows the wave in slow motion (a) What is the length of the pipe? (b) What is the fundamental frequency of this pipe? Hz (c) What is the frequency of the next highest standing wave for this pipe (the next higher harmonic from the one shown in the animation)? Hz

Explanation / Answer

v = 340 m/s

f = 900 Hz

(A) L = 1.25 lambda

and lambda = v / f

L = 1.25 x 340 / 900 = 0.472 m

(B) for fundamental frequency,

L = lambda / 4

lambd = 4 x 0.472 = 1.89 m

f = v / lambda = 180 Hz

(C) then L = (1.25 + 0.5) lambda = 1.75 lambda

lambda = 0.472/1.75 = 0.27 m

f = 340 / 0.27 = 1260 Hz

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