Wave Equation Solutions: ∂²f/∂t² = 10000 ∂²f/∂x²

EC > GATE 2022 > Wave Equation

Consider the following wave equation,
∂²f(x, t)/∂t² = 10000 ∂²f(x, t)/∂x²
Which of the given options is/are solution(s) to the given wave equation?

f(x, t) = e^{−(x−100t)²} + e^{−(x+100t)²}

f(x, t) = e^{−(x−100t)} + 0.5e^−(x+1000t)

f(x, t) = e^{−(x−100t)} + sin(x + 100t)

f(x, t) = e^{j100π(−100x+t)} + e^{j100π(100x+t)}

Correct : c

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