A) amplitude A/2, frequency 2n and wavelength \[\lambda \]
B) amplitude A/2, frequency In and wavelength \[\lambda /2\]
C) amplitude A, frequency n and wavelength \[\lambda \]
D) amplitude A, frequency 2n and wavelength 2\[\lambda \]
Correct Answer: B
Solution :
\[Y=A{{\cos }^{2}}\left( 2\pi n\,t-2\pi \frac{x}{\lambda } \right)\] \[{{\cos }^{2}}\theta =2{{\cos }^{2}}\theta -1\] \[{{\cos }^{2}}\theta =\left( \frac{\cos 2\theta +1}{2} \right)\] \[\therefore \]\[Y=A\left[ \frac{\cos 2\left( 2\pi nt-2\pi \frac{x}{t} \right)+1}{2} \right]\] \[Y=\frac{A}{2}\cos \left[ 2\pi (2n)t-2\pi \left( \frac{2x}{\lambda } \right) \right]+1/2\] Amplitude =A/2, frequency = 2n wavelength\[=\lambda /2\]
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