A transverse wave is represented by the equation y = y₀sin (2π)/(λ)(vt - x) For what value of λ is the maximum particle velocity equal to two times the wave velocity? (a) λ = 2π y₀ (b) λ = (π y₀)/(3) (c) λ = (π y₀)/(2) (d) λ = π y₀

Answer: (d). y = y₀sin ((2π v)/(λ)t - (2π)/(λ)x): vp,max = (2π v y₀)/(λ) (2π v y₀)/(λ) = 2v ⇒ λ = π y₀ So the answer is (d) λ = π y₀.

A transverse wave is represented by the equation y = y₀sin… | NEET 1998 (AIPMT)

Q103NEET 1998 · AIPMTMedium

Progressive Wave Equation

A transverse wave is represented by the equation

$y = y_0\sin\frac{2\pi}{\lambda}(vt - x)$

For what value of $\lambda$ is the maximum particle velocity equal to two times the wave velocity?

Show answer and solution

Answer: (d)

$y = y_0\sin\left(\frac{2\pi v}{\lambda}t - \frac{2\pi}{\lambda}x\right)$ : $v_{p,\max} = \frac{2\pi v y_0}{\lambda}$
$\frac{2\pi v y_0}{\lambda} = 2v \Rightarrow \lambda = \pi y_0$
So the answer is (d) $\lambda = \pi y_0$ .