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The equation y equals A cos to the power of 2 end exponent invisible function application open parentheses 2 pi   n t minus 2 pi fraction numerator x over denominator lambda end fraction close parentheses represents a wave with

  1. Amplitude A/2, frequency 2 n and wavelength lambda divided by 2    
  2. Amplitude A/2, frequency 2 n and wavelength lambda    
  3. Amplitude A, frequency 2 n and wavelength 2 lambda    
  4. Amplitude A, frequency n and wavelength lambda    

The correct answer is: Amplitude A/2, frequency 2 n and wavelength lambda divided by 2


    The given equation can be x written as
    y equals fraction numerator A over denominator 2 end fraction cos invisible function application open parentheses 4 pi n t minus fraction numerator 4 pi x over denominator lambda end fraction close parentheses plus fraction numerator A over denominator 2 end fraction blank open parentheses because cos to the power of 2 end exponent invisible function application theta equals fraction numerator 1 plus cos invisible function application 2 theta over denominator 2 end fraction close parentheses
    Hence amplitude equals fraction numerator A over denominator 2 end fraction and frequency equals fraction numerator omega over denominator 2 pi end fraction equals fraction numerator 4 pi n over denominator 2 pi end fraction equals 2 n
    and wave length equals fraction numerator 2 pi over denominator k end fraction equals fraction numerator 2 pi over denominator 4 pi divided by lambda end fraction equals fraction numerator lambda over denominator 2 end fraction

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