Ncert Exercises & Solutions

34. The displacement of a progressive wave is represented by y = Asin ( $ω$ t —kx), where x is distance and t is time. Write the dimensional formula of (i) $ω$ and (ii) k.

Hint: The argument of the sin function is dimensionless.

Step 1: Find the dimensions of

ω

and k.

As $(ω$ t — kx) should be dimensionless, [ $ω$ t] = [kx] = 1

$\begin{array}{lr} \Rightarrow & [ω] [T] = [k] [L] = 1 \\ \Rightarrow & [ω] = [T^{- 1}] and [k] = [L^{- 1}] \end{array}$

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