Question

y=A sin (ωt – kx); find the dimensional formula of k and ω, where y,A and x are

in metre and t in seconds.

Answer 1

GIVEN:

THE EQUATION IS : y = A sin (wt - kx)

THE ABOVE GIVEN EQUATION IS IN THE FORM : y = A sin theta.

SINCE THETA IS DIMENSIONLESS ; ... wt - kx = [M0L0T0] i.e. = 1

SO, wt = 1 AND ALSO kx = 1.

NOW,

wt = 1 ... [w] = [1/t] = [ T-1]

ALSO;

kx = 1 ... [k] = [1/x] = [ L-1]

SO, [w] =[T-1] AND [k] = [ L-1]

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