The equation y=A ^2 (2 n t-2 x ) represents a wave with - Vidyadip

MCQ

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

✓
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 $2 \lambda$
D
Amplitude $A$, frequency $n$ and wavelength $\lambda$

✓

Answer

Correct option: A.

Amplitude $A / 2$, frequency $2 n$ and wavelength $\lambda / 2$

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

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