Question

A wave is represented by y = a sin(At - Bx + C) where A, B, C are constants and t is in seconds and x is in metre. The Dimensions of A, B, and C are ______.

Options

• [T^-1], [L], [M⁰L⁰T⁰]

• [T^-1], [L^-1], [M⁰L⁰T⁰]

• [T], [L], [M]

• [T^-1], [L^-1], [M^-1]

Answer 1

A wave is represented by y = a sin(At - Bx + C) where A, B, C are constants and t is in seconds and x is in metre. The Dimensions of A, B, and C are [T^-1], [L^-1], [M⁰L⁰T⁰].

Explanation:

y = a sin(At - Bx + C)

Angle has no dimensions. so,

Dimensions of At = [M⁰L⁰T⁰]

⇒ A = [T^-1]

Dimensions of Bx = [M⁰L⁰T⁰]

⇒ B = [L^-1]

Dimensions of C = [M⁰L⁰T⁰]