Question

A transverse wave is represented by y = 2sin (ωt - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be ______.

Options

• 4π

• 2π

• π

• 2

Answer 1

A transverse wave is represented by y = 2sin (ωt - kx) cm. The value of wavelength (in cm) for which the wave velocity becomes equal to the maximum particle velocity, will be 4π.

Explanation:

y = 2sin (ωt - kx)

Maximum particle velocity, v_m = Aω

wave velocity, v_p = `omega/k`

v_p - v_m

`omega/k = Aomega`

k = `1/A = (2pi)/lambda`

λ = 2πA = 2π × 2 = 4π