Question

The equation $y=A{\cos }^2\left(2\pi nt-2\pi \frac{x}{\lambda }\right)$ 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 $\lambda$
• D. Amplitude A, frequency $2n$ and wavelength $\lambda /2$

Answer 1

Answer: (A)

The given equation can be $x$ written as
$y=\frac{A}{2}\cos \left(4\pi nt-\frac{4\pi x}{\lambda }\right)+\frac{A}{2}$
$\left(\because {\cos }^2\theta =\frac{1+\cos 2\theta }{2}\right)$
Hence amplitude $=\frac{A}{2}$ and frequency
$=\frac{\omega }{2\pi }=\frac{4\pi n}{2\pi }$
$=2n$ and wave length $=\frac{2\pi }{k}$
$=\frac{2\pi }{4\pi /\lambda }=\frac{\lambda }{2}$