Question Bank • QB_EM_DE_013 NAT • 2 Marks

Section 1: Engineering Mathematics

Differential Equations

Subtopic: Partial Differential Equations – Laplace, heat and wave equations

Question Statement:

For the one-dimensional wave equation $\frac{\partial^2 u}{\partial t^2} = 9 \frac{\partial^2 u}{\partial x^2}$, the wave propagation speed $c$ in $\text{m/s}$ is equal to ________ (answer in integer).

Answer Key:

3

Step-by-Step Solution & Explanation

The canonical form of the one-dimensional wave equation is: $\frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}$ where $c$ is the wave propagation speed. Comparing coefficients: $c^2 = 9 \implies c = 3 \text{ m/s}$
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