Verify that a given sine function satisfies the one-dimensional wave equation by computing its second-order partial derivatives.

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Verifying a Solution to the Wave Equation

Multivariable calculus warmup

Show that \(f(x, t) = \sin (x + at)\) satisfies the wave equation \(a^2f_{xx} = f_{tt}\).

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What you need first

the chain rule
derivatives of sine and cosine
concept of partial differentiation

What this problem tests

Tests the ability to compute second-order partial derivatives using the chain rule and substitute them into a given equation.

This is a standard introductory problem in multivariable calculus or partial differential equations, demonstrating how to check if a function is a solution to a PDE.

Verifying a Solution to the Wave Equation

What you need first

What this problem tests

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