Question

A wave is represented by the equation $y=A\sin (10\pi x+15\pi t+\frac{\pi }{3})$, where $x$ is in meters and $t$ is in seconds. The expression represents

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

Answer 1

Answer: (B), (C)

a wave travelling in the negative x-direction with a velocity $1.5m/s$
a wave travelling in the negative x-direction with a wavelength $0.2m$

As the expression for displacement is of the form $y=A\sin (kx+wt+\varphi )$ the wave is travelling in -ve x-direction.
If wave is of the form $y=A\sin (kx-wt+\varphi )$ than the wave is travelling in $+ve$ x-direction.
$velocity=\frac{w}{k}=\frac{15\pi }{10\pi }=\frac{3}{2}=1.5\frac{m}{s}$
$\lambda =\frac{2\pi }{k}=\frac{2\pi }{10\pi }=0.2m$