Question

Explain how overtones are produced in an open pipe. Show thatall harmonics are present in the open pipe.

Answer 1

In an open pipe, the waves at the open ends gets reflected to inside by the air pressure from outside.  The phase difference between the reflected and the incident waves will be 0.  The air at the opening has the largest pressure difference, so it will be an antinode.

Thus at the open ends on both sides, there are antinodes.  So the length of the pipe will be a multiple of  λ/2.
     L = n λ/2  ie.,
   λ = 2 L / n            f =  v / λ =   v n /2 L            where n = integer. 1,2, 3 , 4....

thus the frequencies of  v/2L,  2v/2L, 3v/2L, ....  are all present in the open pipe.  

So if an external source of sound like a tuner fork or a whistle, creates sound waves with the same frequency of the above fundamental or overtones of the pipe, then the pipe will vibrate or resonate .  Otherwise the waves inside the pipe will nullify their own energy due to destructive interference.