Question

the displacement of a Wave is represented by y=Asin (Wt-Kx) where x is distance and t is time write the dimensions of W and K

Answer 1

Dimensions of left hand side is always equal to right hand side
only same dimension quantity can be add/ substract to each other
so wt and kx have same direction
here A is amplitude which dimension is [L].
y have also distance which dimension is [L].
so wt=1 also k=1 bcz when we multiply by A which give distance which is equal to y
so w have [T^-1]
k=[L^-1]

Answer 2

[w]=?

[k]=?

(wt-kx) is a dimension less formula

hence,

wt and kx also dimension less

So,

[w]=[T^-1]

[k]=[L^-1]