Question

A simple harmonic wave is represented by the relation $y(x,t)=a_{0}sin2\pi (vt-\frac{x}{\lambda })$ if the maximum particle velocity is three times the wave velocity, te wavelength $\lambda$ of the wave is-

• A. $\pi a_0/3$
• B. $2\pi a_0/3$
• C. $\pi a_0$
• D. $\pi a_0/2$

Answer 1

Answer: (B)

$2\pi a_0/3$

$\begin{array}{c}{V}_p=a_0\left(2\pi V\right)\\ =2\pi a_{0}V\\ V_w=\frac{2\pi V\lambda }{2\pi }=V\lambda \\ \Rightarrow 2\pi a_0=3V\lambda \\ \lambda =\frac{2}{3}\pi a_0\\ Hence,\\ optionBiscorrectanswer.\end{array}$