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The displacement of a progressive wave i...

The displacement of a progressive wave is represented by `y = A sin (omegat - kx),` where x is distance and t is time. Write the dimensional formula of (i) `omega` and (ii) k.

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Now, by the principle of homogeneity, i.e., dimensions of LHS and RHS should be equal,
`"hence "" "[LHS]=[RHS]`
`Rightarrow [L]=[A]=L`
`"As "omegat-kx" should be dimensionless",[omegat]=[kx]=1`
`Rightarrow [omega]T=[k]L=1`
`Rightarrow [omega]=T^(-1) and [k]L=1^(-1)`
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