Question

A transverse wave is described by the equation $y=y_{0}sin2\pi$($ft-\frac{\pi }{\lambda }$). The maximum particle velocity is equal to 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 $\lambda$ = $\frac{\pi y_0}{2}$

A transverse wave is described by the equation,

$y=y_{0}sin2\pi (ft-\frac{\pi }{\lambda })$

The maximum velocity of particle

$v_{max}=y_0.2\pi f$. . . .(1)

The velocity of wave,

$v_{wave}=\lambda f$. . . . .(2)

Given,

$v_{max}=4v_{wave}$

$y_{0}2\pi f=4\lambda f$

$y_0\pi =2\lambda$

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

The correct option is B.