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Topic: Help: Fourier anlysis (transverse waves)
Replies: 1   Last Post: Jul 7, 1996 4:58 AM

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Anthony Hugh Back

Posts: 68
Registered: 12/6/04
Re: Help: Fourier anlysis (transverse waves)
Posted: Jul 7, 1996 4:58 AM
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In article: <4rinf9$6ra@parlor.hiwaay.net> bpdavis@hiwaay.net (Brian P.
Davis) writes:
>
> I've been given a problem, and I'm stumped. My professor has assigned us
> the problem of determing the y value of the following equation when the
> time, t, is not equal to 0.
>
> y = (A cos(wt) + B sin(wt)) sin (wx/c)
>
> I purposely left off the subscripts for readability. A should be A sub n
> B should be B sub n, and the same for y and w.
>
> We know the following information:
> frequency = 100Hz
> length of string = 50cm
> string struck by mallet at 12.5 cm (or length / 4)
> time increment is 0.0001s
>
> I've already done the integration and have equations for A sub n
> and B sub n.
>
> My biggest problem right now is what to do with x. Is it a constant
> value (i.e. length / 4) or do you have to calculate for every possible
> value of x? If the latter is the case, how do you come upon a final
> answer for y? Or am I just way off base?
>
> Thanks for any help,
> Brian
>


I assume that (x,y) are coordinates of points on the vibrating string. In
that case you find the displacement y for any given x. Clearly y will vary
for any value you assign to x, but you find what a particular point on the
string is doing, by entering its x-value in the equation and keeping it
constant while you see what happens to y as t changes. I should have thought
that the x=12.5 point will be used in finding the constant of integration -
but I am not sure how the original equation was derived.

--
Anthony Hugh Back







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