Q. A transverse wave is represented by the equation $y = y_{0}\sin{\frac{2\pi}{\lambda}(vt - x)}$ For what value of $\lambda,$ the maximum particle velocity equal to two times the wave velocity
A) $\lambda = 2\pi y_{0}$
B) $\lambda = \pi y_{0}/3$
C) $\lambda = \pi y_{0}/2$
D) $\lambda = \pi y_{0}$
Explanation
(d) On comparing the given equation with standard equation $y = a\sin{\frac{2\pi}{\lambda}(vt - x)}.$ It is clear that wave speed $(v)_{wave} = v$ and maximum particle velocity $\left( v_{\max} \right)_{particle} = a\omega = y_{0} \times$ co-efficient of $t = y_{0} \times \frac{2\pi v}{\lambda}$
$\because\left( v_{\max} \right)_{particle} = 2(\omega)_{wave} \Rightarrow \frac{a \times 2\pi v}{\lambda} = 2v \Rightarrow \lambda = \pi y_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.