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Questions  

The equation y=acos2(2πnt2πx/λ) represents a wave with

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 2λ
d
amplitude α, frequency n and wavelength Iλ

detailed solution

Correct option is A

Given wave is y=acos2⁡(2πnt−2πx/λ) 2cos2⁡θ=cos⁡2θ+1 or cos2⁡θ=(cos⁡2θ+1)/2 y=acos⁡2(2πnt−2πx/λ)+12 =a2cos⁡4πnt−4πxλ+1 We know that the equation of a wave is given by y=a′cos⁡ω′t−2πxλ′+1 a′=a2, ωt=4πnt or 2πn′t=4πnt  or  n′=2n Further 2πxλ′=4πxλ  or  λ′=λ/2

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