JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Waves & Sound

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 :

Answer: (A)

Solution

The maximum particle velocity is

v_{max} = A ω = 2 ω

cm/s. The wave velocity is

v_{wave} = \frac{ω}{k}

. Setting them equal:

\frac{ω}{k} = 2 ω

gives

k = \frac{1}{2}

. Since

k = \frac{2 π}{λ}

, we have

λ = \frac{2 π}{k} = \frac{2 π}{1/2} = 4 π

cm.

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option