WAVES OF AIR IN A TUBE.
49
dX__dX
du dv
or, more conveniently,
We shall now proceed with the successive steps of
solution.
First step. Neglect all the terms on the right hand.
d2X
Then ^—-j- = 0 ; X (see Partial Differential Equations,
Article 30) = (j> (v) + Ÿ (u). As we propose to consider
only a wave travelling in the direction of x increasing,
Article 24 of this treatise, we shall neglect the second
function, and adopt X = (v).
Second step. Substitute the value cf> (v) for X in
the first term on the right hand, and we have, since
die “
d2X
dv .du
4