Is There an Exponential Relationship in Acoustic Resonance Amplitude Decay?

[Elle90]

Set-up
Closed tube with a hole at each end. Microphone at one end attached to computer. Clap noise made at the other end which will produce a range of frequencies. The computer program detects the resonant frequencies and their amplitudes.

The graph produced seems to show the lower resonant frequencies to have higher amplitudes and I've read that in musical instruments each new 'generation' of harmonic (increasing node number) has a lower amplitude.

On my graph it looks like the amplitude exponentially decays with increasing resonant frequency. Is this correct? Is there an exponential relation that can be seen from wave equations, if so which equation?

 

[Stonebridge]

The harmonics present, and their relative strength/amplitude, is rather complex to analyse.
In musical instruments, the harmonics present and their relative amplitudes depend on a number of factors. Probably the most important being
-the method of excitation of the air
-the shape of the tube
In general, certain harmonics can be favoured by these factors, and the pattern you mention is not "exponential"; though as a general rule, the fundamental is the greatest and higher harmonics have smaller amplitudes.
In your experiment, the diameter of the tube will influence the relative amplitudes of the higher harmonics. This is due to the "end correction"; the fact that the effective length of the pipe depends on its width.
The harmonics present also depend on whether or not the vibrations are forced or natural.
I did a search for something more rigorous but didn't find anything much.
I would suggest in your experimentation that you investigate the effect of using pipes of different width. Or, more accurately, different width to length ratios. You should notice that the relative frequencies of the higher harmonics change.
There is a link here to an article on the voicing/tone quality of organ pipes which goes into this in some detail. You will need to plough through a lot of specialised stuff on organ pipes, but the section (linked) is quite informative.
Remember that organ pipe vibrations are forced.
http://www.pykett.org.uk/how_the_flue_pipe_speaks.htm#Timbre