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, the wavelength $\lambda$ of the wave is

• A. $\frac{\pi a_0}{3}$
• B. $\frac{2\pi a_0}{3}$
• C. $\pi a_0$
• D. $\frac{\pi a_0}{2}$

Answer 1

The correct option is B

$\frac{2\pi a_0}{3}$

Maximum particle velocity $=a_0\omega =2\pi a_{0}v$

Wave velocity $=v\lambda$

Given that $2\pi a_{0}v=3v\lambda$

Or $\lambda =\left(\frac{2\pi a_0}{3}\right)$