May somone please provide an equation for amplitude, harmonic relation
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May somone please provide an equation for amplitude, harmonic relation

[From: ] [author: ] [Date: 11-05-30] [Hit: ]
the amplitudes do not follow a simple pattern; some of the higher frequency harmonics can have a larger amplitude than lower frequency ones.(Also the relative amplitudes change as the vibration decays, so it is not a static picture in practice.). Take a look through the first link, as an example.......
Can anybody give me an equation for the graph at the bottom of this site <>http://paws.kettering.edu/~drussell/Demos/string/Fixed.html> it is the relationship between the amplitude of a wave on a string (Guitar) and the harmonic number of the frequency from the fundamental frequency. All relivant information is on the page.
Thank you in advance for your reply.

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First, the graph is inaccurate (though crudely correct). In reality, the amplitudes do not follow a simple pattern; some of the higher frequency harmonics can have a larger amplitude than lower frequency ones. (Also the relative amplitudes change as the vibration decays, so it is not a static picture in practice.). Take a look through the first link, as an example.

For an ideal case, the relative amplitudes can be calculated. The maths isn't simple through. Take a look at the 2nd link. The 'ideal' frequency distribution for a guitar plucked at the mid-point is also shown (Fig 26) there. The general shape corresponds to your diagram - but the negative values of amplitudes may be confusing - just use their moduli (positive values). So the amplitude of the n-th harmonic is proportional to: |sin(n*pi/2)/[(n*pi/2)^2]| (see equation 285 in link).

Edit: Since sin(n*pi/2) is always 0, 1 or -1. We can simplify and say that the amplitudes (when present) are proportional to 1/n^2. End_edit.
The real graph (spectrum) will be a more complex shape dependent on the design of the guitar - shape, elasticity moduli of neck, body etc. From my (albeit limited) knowledge, I would say the amplitudes for a real guitar cannot be calculated accurately. They would need to be measured using a spectrum analyser.

Hope that helps a bit.
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