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

Solution

Physics sir · 3 steps

Set ω/k equal to Aω. The ω cancels and the amplitude fixes k, so you get λ.

1. Wave velocity. For y = A sin(ω t - kx) the wave moves with speed v = ω/k. Here A = 2 cm.
2. Maximum particle velocity. Each particle moves with velocity (∂ y)/(∂ t) = Aω cos(ω t - kx). Its largest value is Aω = 2ω.

   ω/k = Aω ⇒ k = 1/A = 1/2 cm⁻¹

3. So. λ = 2π/k = 2π × 2 = 4π cm, which is option (a).

The idea to keep. Wave speed is ω/k and peak particle speed is Aω. They are equal exactly when λ = 2π A. Always convert k to λ through λ = 2π/k.

Answer from the NTA final answer key. Solution by PrepWiser.