Question Detail
Question
A sinusoidal wave travelling in the positive direction has an amplitude of 15 cm, wavelength 40 cm and frequency 8 Hz. The vertical displacement of the medium at t=0 and x=0 is also 15 cm. The phase constant δ and expression for wave functions are
Correct Answer
Option B is the correct answer.
Detailed Explanation
The general form is y = A cos(ωt - kx + δ). A = 15 cm. ω = 2πf = 2π(8) = 16π rad/s. k = 2π/λ = 2π/40 = π/20 rad/cm. At t=0 and x=0: y(0,0) = A cos(δ) = 15. Since A = 15, cos(δ) = 1, so δ = 0. The wave function is y = 15 cos(16πt - πx/20).
Hint
The displacement at t=0, x=0 is 15 cm. Use y = A cos(ωt - kx + δ).