Question

What are the speeds of the particles at $x=1.0cm$ at $t=0.011,0.012$ and $0.013s$ ?

Answer 1

For a wave given by $y=Asin(kx-\omega t)$,

Velocity of particles is given by $\frac{dy}{dt}=-A\omega cos(kx-\omega t)$

Thus the velocity of the particle is $v(x,t)=-\frac{\pi }{10}cos\pi [\frac{x}{2.0cm}-\frac{t}{0.01s}]$

Putting the values of x and t in the above equations gives,

$v(1cm,0.011s)=-9.7cm/s$

$v(1cm,0.012s)=-18cm/s$

$v(1cm,0.013s)=-25cm/s$