Which of the following functions represent a wave

(x - v t)^{2}

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log (x + v t)

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e^{- (x - v t)^{2}}

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\frac{1}{x + v t}

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Solution

The correct option is C $e^{- (x - v t)^{2}}$
Although all the four function are written in the form $f (a x \pm b t),$ only option $(c)$ among the four function is finite everywhere at all times. Hence only option $(c)$ represents a wave.

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