Question

A wave is represented by the equation ;
$\, \, \, \, \, y=A \sin (10 \pi x+15 \pi l+ \pi /3) $
where, x is in metre and t is in second. The expression represents

• A. a wave travelling in the positive x-direction with a velocity 1.5 m/s
• B. a wave travelling in the negative x-direction with a velocity 1.5 m/s
• C. a wave travelling in the negative x-direction with a wavelength 0.2 m
• D. a wave travelling in the positive x-direction with a wavelength 0.2 m

Answer 1

Answer: (B), (C)

$\omega=15 \pi ,k=10 \pi $
Speed of wave, $\, \, \, \, \, v=\frac {\omega}{k}=1.5 \, m/s $
Wavelength of wave $\lambda = \frac {2 \pi }{k}= \frac {2 \pi }{10 \pi }=0.2 \, m $
$10 \pi x$ and $15 \pi t$ have the same sign. Therefore, wave is travelling in negative x-direction.
$\therefore $ Correct options are (b) and (c)