Question

When a plane harmonic wave of wavelength $\lambda$ travels in a medium, the particle speed will always be less than the wave if amplitude is,

• A. less that $\frac{\lambda }{2\pi }$
• B. less that $\lambda$
• C. greater than $\frac{\lambda }{\pi }$
• D. greater than $\lambda$

Answer 1

The correct option is A

less that $\frac{\lambda }{2\pi }$

For a plane harmonic wave, the particle displacement is given by

$y=Asin(\omega t-kx)$

Particle speed $V=\frac{dy}{dt}=A\omega cos(\omega t-kx)$

$\therefore V_{max}=A\omega =2\pi Af$

Wave speed $v=f\lambda$

particle speed will always less than wave speed if $2\pi Af<f\lambda$

or $A<\frac{\lambda }{2\pi }$