Question

show that only odd hormonics are present in vibration of air column in a pipe closed at one end​

Answer 1

Answer:

Let's consider a organ pipe closed at one end and open at other end. if a vibrating of tunning fork of frequency held near its open end , it sends longitudinal waves in the pipe , they are reflected from closed end. here the incident and reflected waves interfere and formed stationary wave.

Let length of closed organ pipe is L

wave length of Longitudinal wave is

see figure, length of organ pipe , l = 1/4 × wavelength =

so, fundamental frequency = v/4l , where v is speed of sound.

first overtones , length of organ pipe ,l=

l =

now, frequency of first overtone = 3v/4L

e.g., 1st overtones = 3rd harmonic

similarly, we get 2nd overtone = 5th harmonic

so, nth overtone = (2n + 1)th harmonic

hence ,it is clear that only odd harmonics are present as overtones in the case of an air column vibrating in a pipe closed at one end.

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