Q. The equation $y = A\cos^{2}{(2\pi\ nt - 2\pi\frac{x}{\lambda})}$ represents a wave with
A) Amplitude $A/2,$ frequency $2n$ and wavelength $\lambda/2$
B) Amplitude $A/2,$ frequency $2n$ and wavelength $\lambda$
C) Amplitude $A,$ frequency $2n$ and wavelength $2\lambda$
D) Amplitude $A,$ frequency $n$ and wavelength $\lambda$
Explanation
(a) The given equation can be written as
$y = \frac{A}{2}\cos{\left( 4\pi nt - \frac{4\pi x}{\lambda} \right) + \frac{A}{2}}\ \ \left\lbrack \because\cos^{2}{\theta = \frac{1 + \cos{2\theta}}{2}} \right\rbrack$
Hence amplitude $= \frac{A}{2}$ and frequency $= \frac{\omega}{2\pi} = \frac{4\pi n}{2\pi} = 2n$
And wave length $= \frac{2\pi}{k} = \frac{2\pi}{4\pi/\lambda} = \frac{\lambda}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.