Question

a sinusoidal progressive wave is generated in a string. Its equation is given by y=(2mm) sin(2πx-100πt+π/3). the time when particle at x=4m first passes through mean position will be

Answer 1

We have , y= (2mm)sin(2pix-100pit+ pi/3)
This equation is of the form
y= Asin(kx-wt+phi),
where A =2mm ,k= 2pi, w= 100pi, and
phi = pi/3
So, wave velocity,v = w/k
=> v = 100pi/2pi
=> v = 50m/s
So, at x = 4m, v= 50m/s
t = x/v
=> t = 4/ 50
=> t = 0.08 second