wave_mechanics critical_thinking Question 21
Question: The equation $ y=A{{\cos }^{2}}( 2\pi \ nt-2\pi \frac{x}{\lambda } ) $ represents a wave with
[KCET 2002]
Options:
A) Amplitude A/2, frequency $ 2n $ and wavelength $ \lambda /2 $
B) Amplitude A/2, frequency $ 2n $ and wavelength $ \lambda $
C) Amplitude A, frequency $ 2n $ and wavelength $ 2\lambda $
D) Amplitude A, frequency $ n $ and wavelength $ \lambda $
Show Answer
Answer:
Correct Answer: A
Solution:
The given equation can be x written as $ y=\frac{A}{2}\cos ( 4\pi nt-\frac{4\pi x}{\lambda } )+\frac{A}{2} $
$ ( \because {{\cos }^{2}}\theta =\frac{1+\cos 2\theta }{2} ) $ Hence amplitude $ =\frac{A}{2} $ and frequency $ =\frac{\omega }{2\pi }=\frac{4\pi n}{2\pi }=2n $ and wave length $ =\frac{2\pi }{k}=\frac{2\pi }{4\pi /\lambda }=\frac{\lambda }{2} $ .
BETA
