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.
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.
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.