First slide

Travelling wave

Question

The equation $y = {Acos}^{2} (2 πnt - 2 π \frac{x}{λ})$ represents a wave with

Easy

A

Amplitude A/2, frequency 2n and wavelength $λ / 2$
B

Amplitude A/2, frequency 2n and wavelength $λ$
C

Amplitude A, frequency 2n and wavelength $2 λ$
D

Amplitude A, frequency n and wavelength $λ$

Solution

The given equation can be written as
$y = \frac{A}{2} \cos (4 πnt - \frac{4 πx}{λ}) + \frac{A}{2} (∵ \cos^{2} θ = \frac{1 + \cos 2 θ}{2})$
Hence amplitude = $\frac{A}{2}$ and frequency $= \frac{ω}{2 π} = \frac{4 πn}{2 π} = 2 n$
and wave length $= \frac{2 π}{k} = \frac{2 π}{4 π / λ} = \frac{λ}{2}$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App