Question

A traverse wave is given by $y=a\sin 2\pi (ft-x/\lambda )$. The maximum particle velocity is four times the wave velocity, when

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

Answer 1

The correct option is D $\lambda =\pi a/2$

The wave velocity is $v=f\lambda$ and the maximum particle velocity is $2\pi af$. So, $4f\lambda =2\pi af\Rightarrow \lambda =\frac{\pi a}{2}$.