The displacement of a progressive wave is represented by $y = A s i n (ω t - k x)$ ,
where 𝑥 is distance and 𝑡 is time. Write the dimensional formula of (𝑖) $ω$ and (𝑖𝑖) $k$ .

Question

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

Toppr Admin · Accepted Answer

We have to apply principle of homogeneity to solve this problem. Principle of homogeneity states that in a correct equation, the dimensions of each term added or subtracted must be same, i.e., dimensions of $$LHS$$ and $$RHS$$ should be equal.
According to the problem
$$y=A\, sin(\omega t-kx)$$
Here, $$y=[L]$$ hence
$$A\, sin (\omega t-kx)=[L]$$
Here,$$A=[L]$$,which peak value of y
So,$$\omega t-kx$$ should be dimensionless.
i) $$[\omega t]$$=constant
$$\Rightarrow [\omega]=[T^{-1}]$$
ii) $$[kx]$$=constant
$$\Rightarrow [k]=[L^{-1}]$$

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