When a wave traverses a medium,the displaceme | vedclass

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(D) Given the wave equation: $y = a \sin (bt - cx)$.In the expression $y = a \sin (	heta)$,the argument of the trigonometric function $	heta = (bt -

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$\frac{b}{c}$

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(D) Given the wave equation: $y = a \sin (bt - cx)$.In the expression $y = a \sin (	heta)$,the argument of the trigonometric function $	heta = (bt - cx)$ must be dimensionless.Since $bt$ and $cx$ are added/subtracted,they must have the same dimensions as the argument of the sine function,which is dimensionless.$(a)$ $\frac{y}{a}$ is the ratio of two lengths,so it is dimensionless.$(b)$ $bt$ is the argument of the sine function,so it is dimensionless.$(c)$ $cx$ is the argument of the sine function,so it is dimensionless.$(d)$ The dimension of $b$ is $[T^{-1}]$ and the dimension of $c$ is $[L^{-1}]$.Therefore,the dimension of $\frac{b}{c} = \frac{[T^{-1}]}{[L^{-1}]} = [LT^{-1}]$,which represents the dimension of velocity.Thus,$\frac{b}{c}$ is a quantity with dimensions.

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?

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