Q34 of 44 Page 9

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

Given:


Equation for wave y = A sin(ωt – kx)


We know that the argument for the sine function is always in degrees or radians and therefore dimensionless. And we know that only dimensionally like quantities can be added or subtracted, therefore the quantities ωt and kx must be dimension less, therefore



but t =



Similarly,



But x =



Therefore, the dimensional formulas are (i) ω = [M0L0T-1] and (ii) k =[M0L-1T0]


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