Question

A transverse wave is described by the equation $Y=Y_0\sin 2\pi (ft-x/\lambda )$. The maximum particle velocity is equal to four times the wave velocity if?

• A. $\lambda =\pi Y_0/4$
• B. $\lambda =\pi Y_0/2$
• C. $\lambda =\pi Y_0$
• D. $\lambda =2\pi Y_0$

Answer 1

The correct option is B $\lambda =\pi Y_0/2$

A transverse wave is described in equation

$Y=Y_{0}sin2\pi (ft-x\lambda )$

The maximum velocity of the particle

$v_{max}=amplitude\times 2\pi f=Y_0\times 2\pi f$

Velocity of wave $v_{wave}=\lambda \times f$

condition of the problem

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

$\Rightarrow Y_0\times 2\pi f=4\times \lambda \times f$

$\Rightarrow \lambda =\frac{\pi Y_0}{2}$

Answer B: