# A STUDY OF WAVE EQUATION BY SEPARATION OF VARIABLES

### Abstract

**Objective: **In this paper we focus our study on wave equations. Westudying the solution of wave function by using separation of variables technique. The functions of several variablesand having worked through the concept of a partial derivative.

**Materials and Methods:**We first formulate the wave function u(x,t) where x is length of string. Solving the equation???? ????, ???? = ???? ???? ????(????) in twovariables byusing the methods of Partial Differential Equation. We get the following equation where k is constant.

**Results: **We are going to check the possible for the constant k in the above equation. First we consider k = 0 then we get

u x, t = (px+r) (at+b) where a,b, p and r, were constants.

Secondly we consider k> 0 then we get

*x x **F x Ae Be *w -w ( ) = + whereA and B are constants and w = *k *.

was used isidentified by the subscript in *u *(*x*, *t*) *n *and *n *l , and arbitrary constants are C and D.

**Conclusion:**The solutions given in the first two cases are dull solutions.The solution given in the last case really does satisfy the wave equation. We

can find a particular solution function for varying values of time, t,

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