GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/14

Question 14 (Textile Technology & Fibre Science)

Suppose u(x,t) = \frac{1}{2}[g(x+ct)+g(x-ct)] is a solution of the following initial value problem of the wave equation
u_t_t = 9u_x_x, u(x,0) = g(x), u_t(x,0)=0.
Then the value of c^2 is _____________.

Answer / Solution

As we know the wave equation-

\frac{\delta^2 u}{\delta t^2}=C^2 \times \frac{\delta^2 u}{\delta x^2}

Compare with the above equations-

u_t_t = 9u_x_x

C^2=9 (Ans)

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