The first two times are 0.000169 s and 0.001724 s.

[ndnassif]

A wave on a string is described by the equation y = 0.150 m sin(1.795 x + 2010.6 t).

Two questions:

1. How do I find wave speed?

velocity = λ * f​

My pathway λ → (2pi/λ) = 1.795 ... λ = 3.50m​

My pathway f → f = (ω/2pi) ... ω = 2010.6 ... f = 320 Hz​

velocity = λ * f ... velocity = (3.50m)*(320Hz) = -1120m/s (Motion→Left)​

2. What are the first two times when the vertical position is y = 0.050 m?

Not sure how to go about this...​

 

[haruspex]

1. You have sin(1.795 x + 2010.6 t).
If you evaluate for any pair (x, t), and also for pair (x-2010.6, t+1.795), you must get the same result. I.e. wave is moving in the -ve x direction at speed 2010.6/1.795.

2. 0.05 = 0.150 sin(1.795 x + 2010.6 t)
You don't say what x to use here, so I'll take it as zero.
0.05 = 0.150 sin(2010.6 t)
1/3 = sin(2010.6 t)
arcsin(1/3) = 0.3398... I'll use 0.34
2010.6 t = 0.34 + 2n.pi or pi - 0.34 + 2n.pi
The two smallest non-negative solutions are both with n = 0:
0.34, pi - 0.34
So t = 0.34/2010.6, (pi - 0.34)/2010.6