Harmonics: Obtaining, Stationary Waves & Probability

[sachin123]

When are harmonics obtained?
Consider an open pipe.
Take a vibrating tuning fork and place it above the pipe.
Then what harmonic is obtained for the stationary wave?
Is the fundamental or the second or what?
I am asking if the harmonic is a matter of probability.
Thank You.

 

[Stonebridge]

Generally, you get all the possible harmonics present in a wave. The fundamental is usually the one with greatest amplitude (and energy), with each higher harmonic having a smaller amplitude.
You tend hear the fundamental as the pitch of the note, even if it has a smaller amplitude than some of the higher harmonics. The other harmonics combine to colour the note and give it its characteristic timbre.

In the case of the tuning fork, you are causing resonance where the fork has the same frequency as one of the natural harmonics of the pipe. In this case you tend to hear that harmonic as the pitch of the pipe.

So if your fork has a frequency of 200Hz and the pipe has a fundamental of 100Hz, you would get a resonance at the 2nd harmonic. (For a pipe open at both ends)

 

[sachin123]

Thank You
So,even in the case of tuning fork,all the harmonics exist and we tend to hear the 2nd one(as in your example)?

 

[Stonebridge]

Yes. The human ear (and brain) makes a number of assumptions about sounds. We tend to hear the lowest natural frequency of the pipe (fundamental) as the pitch of the note.
Some experiments were done some time back, where the fundamental was removed, but the other harmonics were left intact. People still tended to "hear" the fundamental. It seems the brain can reconstruct this frequency from the harmonic series.
In the case of the tuning fork and pipe; you would be exciting that one frequency to a much greater amplitude than the others. A closer analysis of the sound produced would no doubt detect the presence of small amounts of the other natural frequencies. Exactly which and how much would depend on a number of other factors such as the diameter of the pipe. (This is due to the so-called "end correction" of the pipe, where it appears to be longer than it actually is from the point of view of the sound wave.)
There is quite an interesting long article here
http://www.pykett.org.uk/how_the_flue_pipe_speaks.htm
which is worth wading through if you are interested in how pipes, in particular organ pipes, behave.