Question

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 $\lambda$

Answer 1

The correct option is A Amplitude $A/2$, frequency $2n$ and wavelength $\lambda /2$

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