Velocity and frequency of standing waves, number of nodes

AI Thread Summary
The discussion centers on calculating the velocity and frequency of standing waves on a string fixed at one end. To find the velocity, the tension in the string must be determined, which can be derived from the forces acting on the string. The frequency for generating a wave with four nodes corresponds to the second harmonic, where the formula f = n * (v/2L) applies. The general equation for standing waves can be derived by combining the two traveling wave equations using trigonometric identities. Overall, understanding the relationship between tension, frequency, and wave properties is crucial for solving the problem.
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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.
 
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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.
 
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