Question

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

Options

• `(pi"A")/2`

• πA

• 2πA

• A

Answer 1

2πA

Explanation:

y = A sin (ωt - kx)

Particle velocity,

v_p = `"dy"/"dt"` A ωcos (ωt - kx)

∴ (v_p)_max = Aω

wave velocity = `omega/"k"` 

∴ A ω = `omega/"k"`

i.e., A = `1/"k"` But k = `(2pi)/lambda`

∴ λ = 2πA