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

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

Answers (1)

According to the principle of homogeneity dimensional formula on L.H.S. & R.H.S. is equal.

Thus, the dimension of A \; \sin (\omega t - kx) = Dimension of y

\omega t - kx has no dimensions because it is an angle of sin.

\frac{2\pi }{T}t=Kx

[M^{0}L^{0}T^{0}] = k[L]

Thus, \omega has no dimension & dimension of k=[M^{0}L^{-1}T^{0}].

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