Wave Velocity Calculation: y = 0.02 sin[ pi(30x - 400t)] in SI units

[sugz]

Homework Statement

For a wave described by y = 0.02 sin[ pi(30x - 400t)] (SI units), the velocity of the wave (in m/s) is

a) 3/40 b) 40/3 c) (60pi)/400 d)400/(60pi) e) 400

Homework Equations

The Attempt at a Solution

I found the derivative of the function as v= -25.132 cos[pi(30x-400t)] so I assumed the velocity is 25.132 m/s which is none of the options and the correct answer is 40/3.

 

[lightgrav]

they wanted the velocity of the disturbance along the string, not the maximum velocity for one point on the string.
the velocity is hiding in the trig function's argument (kx-ωt) ≈ k(x-vt)

 

[sugz]

That makes sense! So right now the kx-ωt is (30pi)x-(400pi)t, where k= 30pi. So factoring out 30pi we get v=(400pi)/(30pi) which is 40/3. Thank you!