OnlineCBT
Physics · UNITS AND MEASUREMENT
हिन्दीIn a wave equation, the displacement \( y \) of a wave as a function of time \( t \) and distance \( x \) is given by \( y = A e^{-\alpha t} \sin(\beta x - \gamma t) \). The dimensional formula of \( \frac{\gamma}{\beta} \) is equivalent to which of the following physical quantities?
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Correct answer · Option B
Speed
Explanation
The argument of a trigonometric function must be dimensionless. Thus, \( [\beta x] = [1] \implies [\beta] = [L^{-1}] \) and \( [\gamma t] = [1] \implies [\gamma] = [T^{-1}] \). Therefore, \( [\gamma/\beta] = \frac{[T^{-1}]}{[L^{-1}]} = [L T^{-1}] \), which represents speed.
