Question

A transverse wave is described by the equation $y=Asin2\pi (nt-x/{\lambda }_0)$. The maximum particle velocity is equal to 3 times the wave velocity if

Answer 1

A transverse wave is described by equation

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

The max velocity of particle will be

$V_{max}=amplitude\times 2\pi f=y_0\times 2\pi t$

velocity of wave $V_{wave}=\lambda t$

$V_{max}=4V_{wave}$

$\therefore y_0\times 2\pi t=4\times \lambda \times f$

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