GATE 2019 BT – Question 22

Engineering Mathematics · Differential Equations: First order ODEs, higher order ODEs with constant coefficients, Cauchy and Euler equations, Laplace transforms · 1 mark · Multiple choice

Which is a one-dimensional wave equation?

$u_t=c^2u_{xx}$
$u_{tt}=c^2u_{xx}$
$u_{tt}=c^2u_x$
$u_{tt}+u_{xx}=0$

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Show answer and explanation

Correct answer: (B) $u_{tt}=c^2u_{xx}$

Explanation

The classical one-dimensional wave equation has second derivatives in time and space with positive wave-speed square: $\partial^2u/\partial t^2=c^2\partial^2u/\partial x^2$. Thus B. A is diffusion-like, C has the wrong spatial order, and D has the elliptic rather than hyperbolic sign arrangement.

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