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 1200 Hz. The animation shows the wave in slow motion.

(a) What is the length of the pipe?
m

(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

Speed = frequency * wavelength

wavelength = speed/wavelength = 340/1200 = 0.283m

from the animation it is seen that the pattern is at the 5th harmonics

L = 5/4 lamda = 5/4*0.283

L = 0.35 m

B) fundamental frequency = 5v/4L = 5*340/4*0.35 = 1200Hz

C) next harmonics is the 6th harmonics

so f = 6v/4L = 6*340/4(0.35) = 1457.14Hz

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