Question

A transverse wave is described by the equation $Y=y_{0}sin2\pi (ft-\frac{x}{\lambda })$. The maximum particle velocity is four times the wave velocity if

• A. $\lambda =\frac{\pi y_0}{4}$
• B. $\lambda =\frac{\pi y_0}{2}$
• C. $\lambda =\pi y_0$
• D. $\lambda =2\pi y_0$

Answer 1

The correct option is B

$\lambda =\frac{\pi y_0}{2}$

Maximum particle velocity = 4 wave velocity

$A\omega =4f\lambda y_{0}2\pi f=4f\lambda \lambda =\frac{\pi y_0}{2}$