Question

A plane progressive wave is represented by the equation $y=0.25\cos (2\pi t-\pi x)$. The equation of a wave with double the amplitude and half the frequency but travelling in the opposite direction will be

• A. $y=0.5\cos (\pi t-\pi x)$
• B. $y=0.5\cos (\pi t+\pi x$
• C. $y=0.25\cos (\pi t+2\pi x)$
• D. $y=0.5\cos (2\pi t+2\pi x)$

Answer 1

Answer: (B)

$y=0.5\cos (\pi t+\pi x$

$\omega =2\pi t,$
$\omega =2\pi$
$f_1=1$
$f_2=\frac{1}{2}$
$\omega =\pi$
$A_1=0.15$
$A_2=2A_1$
$=0.5$
$y=0.5\cos ({\omega }_{2}t+kx)$
$y=0.5\cos (\pi t+\pi x)$