Velocity and frequency of standing waves, number of nodes

[maiamorbific]

Homework Statement

A string of mass .03 kg and length 2 m is fixed at one end, and driven with an oscillator at the other end. The oscillator induces traveling waves on the string of the form y=A sin (kx-ωt) which traveled down the string, hit the fixed end, and get reflected back as a wave with the form y=Asin (kx+ωt).
I'm asked to find the a.) velocity of the waves, b.)frequency required to generate a wave with 4 nodes, and c.) derive a general equation for standing waves on a string using the two above equations.

Homework Equations

m = 0.03 kg and L = 2 m
λ = 2L = 4 m
k = 2π/λ = π/2
µ = m/L = 0.015 kg/m

The Attempt at a Solution

a.) All the equations I know to find velocity involve either tension or frequency or another variable that I don't have. How do I find the velocity with what I'm given?

b.) I think that 4 nodes is the 2nd harmonic frequency (?) where n=2 in the equation
f = n * (v/2L). Is this right? If so, I can easily find it when I have the answer for velocity.

c.) I think that for this part, I just add the two equations together. I'd call one y1 and the other y2. y1 + y2 = general equation?
[sin a + sin ß = 2 sin ((a+ß)/2) cos ((a-ß)/2)]

My main question is for the (a) part.
Thank you.

 

[maiamorbific]

Would you use sum of the forces = tension - (mg) = 0?
Then I'd solve for tension and use the linear density found above to calculate the velocity.
I think.