Bauhaus-Universität Weimar

On sound and atmospheric vibrations, with the mathematical elements of music
Airy, George Biddell
Making this = 0 when x — 0 and when x — l, 
' (at) — (at) = 0 
(ft (at — — (at + T) = 0, 
which are the terminal equations for this case. 
The first equation, which is general for all values of 
t, gives = <£>'. The second gives 
' is a periodical 
function, going through all its changes while the quan¬ 
tity affected by it is changed by 21, or while t increases 
by — : giving the same number of complete vibrations 
per second, and therefore the same fundamental note, as 
a pipe closed at both ends, Article 78. The velocity of 
the particle, or 
a. <£' (at — x) + a yjr' (at + x), 
may be represented (for the same reasons as in the 
beginning of Article 74) by 
^ ( n . nir (at — x)) 
2 I<7*. sin-^-j- 
, * {-n nnr(at — x)) 
+ 2\Dn. cos —-4 
, v f n • nir (at + a?)] 
+ 2 j Cn . Bin--4 
^ nir (at + x) 
+ S \Dn. cos-j--


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