Question

The equation $y = A \cos ^{2}\left(2 \pi n t-2 \pi \frac{x}{\lambda}\right)$ represents a wave with

• A. Amplitude $A / 2$, frequency $2 n$ and wavelength $\lambda / 2$
• B. Amplitude $A / 2$, frequency $2 n$ and wavelength $\lambda$
• C. Amplitude A, frequency $2 n$ and wavelength $\lambda$
• D. Amplitude A, frequency $2 n$ and wavelength $\lambda / 2$

Answer 1

Answer: (A)

The given equation can be $x$ written as
$y=\frac{A}{2} \cos \left(4 \pi n t-\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
$=\frac{\omega}{2 \pi}=\frac{4 \pi n}{2 \pi}$
$=2 n$ and wave length $=\frac{2 \pi}{k}$
$=\frac{2 \pi}{4 \pi / \lambda}=\frac{\lambda}{2}$