The displacement of a progressive wave is represented by y= A sin (omegat-kx) where x is distance and t is time. Write the dimensional formula of (i) w and (ii) k.

The displacement of a progressive wave is represented by y= A sin (ome

1.	The displacement of a progressive wave is represented by y= A sin (omegat-kx) where x is distance and t is time. Write the dimensional formula of (i) w and (ii) k.
Answer» Solution :Now [LHS]= [RHS] `[y]=[A]=L` because `OMEGAT- KX` is DIMENSIONLESS, `[kx]=M^(0)L^(0)T^(0) "" :. [omega t]=M^(0)L^(0)T^(0)` `:. [K]L=M^(0)L^(0)T^(0) "" :. [omega]T=M^(0)L^(0)T^(0)` `:. [k]=L^(-1) "" :. [omega]=T^(-)`