Question

Displacement equation for a wave is y = a sin (At - B + C), where A, B and C are constants. Determine the dimensions of these constnats.

Answer 1

∵ Angle is a dimensionless quantity.

∴ At - Bx + C = dimensionless quantity = 1

∴ At = dimensionless = 1

∴ A = \(\frac{1}{t} = \frac{1}{T^1} = T^{-1}\)

Hence, dimensional formula of A = [M⁰L⁰T^-1]

Similarly Bx = 1 ⇒ B = \(\frac{1}{x}\)

∴ Dimensional formula of B = [M⁰L^-1T⁰]

and C = 1

∴ Dimensional formula of C = [M⁰L⁰T⁰]