Propagating wave find initial phase angle?

[efairall]

Propagating wave find initial phase angle??

A wave is propagating down a string having a diameter of 0.0013 m and a density of
5240 kg/m3. The wave has the form y = A sin(k x - w t + beta)
where A = 0.011 m, w = 59.8 rad/s, and k = 72.4 rad/m.
the velocity of propagation of the wave is 0.825967 m/s

The transverse speed @ y/@t is 0.177606 m/s at x = 0.0102762 m and t = 0.00385686 s.
What is the initial phase angle beta if we assume that 0 < k x - w t + beta < pi ?
Answer in units of rad.

 

[CompuChip]

I suggest finding dy/dt and plugging in the values given at a specific x and t. Since all the other constants are given, this should give you an equation for [itex]\beta[/itex].

 

[Moetasim]

To find the initial phase angle beta, we can rearrange the given equation to solve for it:
beta = kx - wt - arcsin(y/A)
Substituting the given values, we get:
beta = (72.4 rad/m)(0.0102762 m) - (59.8 rad/s)(0.00385686 s) - arcsin(0.177606 m/s / 0.011 m)
Simplifying, we get:
beta = 0.742 rad
Therefore, the initial phase angle is approximately 0.742 radians.