First slide

Characterstics of wave

Question

The equation $y = {acos}^{2} (2 πnt - 2 πx / λ)$ represents a wave with

Moderate

A

amplitude $α$ /2 frequency 2 n and wavelength $λ$ /2
B

amplitude $α$ /2, frequency 2 a and wavelength $λ$
C

amplitude $α$ , frequency 2 n and wavelength 2 $λ$
D

amplitude $α$ , frequency n and wavelength I $λ$

Solution

Given wave is
$y = {acos}^{2} (2 πnt - 2 πx / λ) 2 \cos^{2} θ = \cos 2 θ + 1 or \cos^{2} θ = (\cos 2 θ + 1) / 2 y = a [\frac{\cos 2 (2 πnt - 2 πx / λ) + 1}{2}] = \frac{a}{2} [\cos (4 πnt - \frac{4 πx}{λ}) + 1] We know that the equation of a wave is given by y = a^{'} [\cos (ω^{'} t - \frac{2 πx}{λ^{'}}) + 1] a^{'} = \frac{a}{2}, ωt = 4 πnt or 2 {πn}^{'} t = 4 πnt or n^{'} = 2 n Further \frac{2 πx}{λ^{'}} = \frac{4 πx}{λ} or λ^{'} = λ / 2$

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