When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a\sin(bt - cx)$, where $a,\ b$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions

Question

Dr. Abubacker · Accepted Answer

Given equation , $y = a\sin{(bt - cx)}$ Comparing the given equation with general wave equation $y = a\sin\left( \frac{2\pi t}{T} - \frac{2\pi x}{\lambda} \right),$ We get $b = \frac{2\pi}{T},\ c = \frac{2\pi}{\lambda}$ Dimension of $\ \frac{b}{c}$ $= \frac{2\pi/T}{2\pi/\lambda} = \left\lbrack LT^{- 1} \right\rbrack,$ and other three quantity is dimensionless

Q. When a wave traverses a medium, the displacement of a particle located at $x$ at a time $t$ is given by $y = a\sin(bt - cx)$, where $a,\ b$ and $c$ are constants of the wave. Which of the following is a quantity with dimensions

Explanation

Reviewed by Dr. Abubacker

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