What does this have to do with noise control? Well, along a one-dimensional path, the wave propagation has to satisfy these equations.

If *f* is an arbitrary function,
a forward going pressure wave will take the form *p*(*x*,*t*)=*f*(*x* - *c t*)
because
(1.) it satisfies the wave equation, and (2.) the argument
*x* - *c t* will remain a constant if and only if as *t* increases, *x* does
also proportionally. Hence, as time increases, the function will
produce the same value only for increasing *x*.

If you are in doubt, plug an example function, such as , into the wave equation and do the derivatives. A forward going pulse is shown in this ANIMATION.

Similarly if *g* is another arbitrary function,
a backward going pressure wave will take the form *p*(*x*,*t*)=*g*(*x* + *c t*)
because
(1.) it also satisfies the wave equation, and (2.) the argument
*x* + *c t* will remain a constant if and only if as *t* increases,
*x* decreases proportionally.
Here as time increases, the function will produce the same value
for decreasing *x*.

A simple example of a function for a backward going wave would be . A backward going wave pulse is shown in this ANIMATION.

Tue Feb 25 21:24:33 EST 1997