Question

A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = (1.8 x 10-3)cos[π(13x - 60t)], where all quantities are in SI units. What is the maximum speed of a particle of the string

Answer 1

Answer:

The maximum speed of a particle of the string is 0.34 m/s

Explanation:

The equation for the vertical displacement y of the string is given by y :

$y=1.8\times 10^{-3}cos[\pi(13x-60t)]$.............(1)

The general equation of transverse wave is given by :

$y=A(kx-\omega t)$.............(2)

On comparing equation (1) and (2) we get,

$\omega=60\pi$

Speed of a particle of the string is maximum when displacement is equal to zero. Maximum speed is given by :

$v_{max}=A\omega$

Where, A = amplitude of wave

$\omega=60\pi$

So, $v_{max}=1.8\times 10^{-3}\times 60\pi$

$v_{max}=0.34\ m/s$

Hence, this is the required solution.