Question

The equation for a wave travelling in x-direction on a string : $y=\left(3.0cm\right)sin\left[\right(3.14x)-(314t\left)\right]$

Find the maximum velocity of a particle of the string

Find the acceleration of a particle at x = 60 cm at time = 0.11 s

Answer 1

Equation of ave is $y=3.0\sin \left[\right(3.14x)-3.14t)]$

here $k=3.14,\omega =314$

so wave velocity $=\frac{\omega }{k}=\frac{314}{3.14}=100cm/s$

acceleration of particle is given by

$a_p=\frac{{\partial }^{2}y}{\partial t^2}=-3.0\times {314}^2\sin \left[\right(3.14x)-(314t\left)\right]$

Acceleration of particle at $x=60cm$,$k=0.11s$

$a_p=-3.0\times {\left(314\right)}^2\sin \left[\right(3,14\times 60)-(314\times 0.11\left)\right]\simeq 230.6m/s$