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