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Question
The displacement of a progressive wave is represented by y = A sin(ωt – kx), where x is distance and t is time. Write the dimensional formula of (i) ω and (ii) k.
Solution
Now, by the principle of homogeneity, i.e., dimensions of LHS and RHS should be equal,
Hence [LHS] = [RHS]
⇒ [L] = [A] = L
As ωt – kx should be dimensionless, [ωt] = [kx] = 1
⇒ [ω]T = [k]L = 1
⇒ [ω] = T–1 = [k] = L–1
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