Question

A sinusoidal wave is propagating in negative x-direction in a string stretched along x-axis.A particle of string at $x=2cm$ is found at its mean position and it is moving in positive y-direction at $t=1s.$ The amplitude of the wave, the wavelength and the angular frequency of the wave are $0.1m,\pi /4m$ and $4\pi rad/s,$ respectively.
The equation of the wave is

• A. $y=0.1sin\left(4\pi \right(t-1)+8(x-2\left)\right)$
• B. $y=0.1sin\left(\right(t-1)-(x-2\left)\right)$
• C. $y=0.1sin\left(4\pi \right(t-1)-8(x-2\left)\right)$
• D. none of these

Answer 1

The correct option is A $y=0.1sin\left(4\pi \right(t-1)+8(x-2\left)\right)$

The equation of wave moving in negative x-direction, assuming origin of position at $x=2$ and origin of time (i.e., initial time) at $t=m1s.$
$y=0.1sin(4\pi t+8x)$
Shifting the origin of position to left by 2 m , to $x=0$ Also shifting the origin of time backwards by 1 s, that is to $t=0s.$
$y=0.1\left[4\pi \right(t-1)+8(x-2\left)\right]$