A transverse wave is represented by y = a sin (?t – kx). For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

Options

(a) πA / 2
(b) π A
(c) 2π A
(d) A

Correct Answer:

2π A

Explanation:

y = A sin ( ?t – kx ) particle velocity,
vₚ = dy/ dt = A ? cos ( ?t – kx )
vₚ ₘₐₓ = A ? wave velocity = ? / k
A ? = ? / k i.e., A = 1/k But k = 2π / λ
λ = 2π A