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Consider the following wave equation,

$$\frac{\partial^{2}f(x, t)}{\partial t^{2}} = 10000 \frac{\partial^{2}f(x, t)}{\partial x^{2}} $$

Which of the given options is/are solution(s) to the given wave equation?

- $f(x, t) = e^{ – (x-100t)^{2}} + e^{ – (x+100t)^{2}}$
- $f(x, t) = e^{ – (x-100t)} + 0.5e^{ – (x+1000t)}$
- $f(x, t) = e^{ – (x-100t)} + \sin (x + 100t)$
- $f(x, t) = e^{ j 100 \pi (- 100x + t)} + e^{ j 100 \pi (100x + t)}$