Question

Prove that the equation y = a sin omegat does not satisfy the wave equation and hence it does not represent a wave.

Answer 1

• A sinusoidal wave must be in the form of y=A sin( kx −ωt) ....(1)

• But we are given

        y= a sin(ω  t)......(2)

• On comparing we find that given equation has no kx term.

        This means that k is zero.

        Which is not possible

• $V = \frac{\omega }{K}$

​         Velocity will become infinite but at no point, does a wave     have infinite velocity. This contradicts the definition of wave.

• Hence k can never be zero and so, there has to be a kx term in any wave equation.

• Hence, given equation does not represent a wave as k=0.

Answer 2

We, have y = a*sinwt , where a is the amplitude , w is the angular frequency and t is time period.

•) Now have to show that y = a*sinwt will not represent a wave .

Now we know that wave equation is d"y/d"t = c^2*d"y/d"x

•) Now putting value of y in the wave equation and doing double differentiation , we get

-a*sinwt = 0

•) Hence LHS ≠ RHS , this implies that wave equation is not satisfied , hence , y = a*sinwt doesn't represent a wave .