The wave equation is given by Y = A sin omega | vedclass

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(B) In the given wave equation $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,the argument of the sine function must be dimensionless.Furthermore,

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$T$

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(B) In the given wave equation $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,the argument of the sine function must be dimensionless.Furthermore,terms inside the parentheses must have the same dimensions to be subtracted.Therefore,the dimension of $k$ must be equal to the dimension of $\frac{x}{v}$.Dimension of $x$ (length) is $[L]$.Dimension of $v$ (velocity) is $[LT^{-1}]$.Thus,the dimension of $k = \frac{[L]}{[LT^{-1}]} = [T]$.

The wave equation is given by $Y = A \sin \omega \left( \frac{x}{v} - k \right)$,where $\omega$ is the angular velocity and $v$ is the linear velocity. What is the dimension of $k$?

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