Question

The equation for a wave travelling in x-direction on a string is : y = 3(sin3.14x-314t),then

Find the maximum velocity of particle of the string .

Answer 1

Equation of travelling wave is $y=3\sin \left[\right(3.14c{m}^{-1}x)-(314s^{-1}t\left)\right]$

From the above equation,

$\omega =314$

$2\pi \nu =314$

$\nu =50Hz$

$k=3.14c{m}^{-1}=314m^{-1}$

$\frac{2\pi }{\lambda }=314$

$\lambda =\frac{2}{100}m=\frac{1}{50}m$

So, velocity

$v=\nu \lambda$

$v=50\times \frac{1}{50}$

$v=1m/s$