Question

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

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

Answer 1

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

Given:
$y=A{\cos }^2(2\pi nt-2\pi \frac{x}{\lambda })$
As we know,
$({\cos }^2\theta =\frac{1+\cos 2\theta }{2})$
Hence above equation can be written as,
$y=\frac{A}{2}\cos (4\pi nt-\frac{4\pi x}{\lambda })+\frac{A}{2}$
Hence, by comparing it with the general equation we get,
ammplitude $=\frac{A}{2}$
frequency $=\frac{\omega }{2\pi }=\frac{4\pi n}{2\pi }=2n$
wavelength $=\frac{2\pi }{k}=\frac{2\pi }{\frac{4\pi }{\lambda }}=\frac{\lambda }{2}$
Final answer: $\left(a\right)$