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**1. Homework Statement**

A 2.5 m long string that has a mass of 0.10 kg is fixed at both ends and is under a tension 30 N. (c) Determine the maximum speed of a point on the middle of the string.

**2. Homework Equations**

2 sinusoidal waves having same amplitude, frequency and wavelength / superposition

y(x, t) = 2Asin(kx)cos(wt)

**3. The Attempt at a Solution**

I have no idea as to what to do to approach this. The point on the string is moving in simple harmonic motion, which can be modeled by y(x) = Asin(wt) and v(x) = Awcos(wt)

so maximum velocity would be Aw. Is this right? how would you find A? I'm probably approaching this wrong. Could someone give me a hint?

For parts (a) we had to solve for the speed of the waves on string, which was

v = (T/u)^(1/2) = (30/0.04)^(1/2) = 27.39 m/s

for part (b) the question was "when the nth harmonic is excited, there is a node 0.50 m from one end. what is n?

wavelength = 2L/n

distance between nodes = wavelength / 2 = 0.5

wavelength = 1 m

1 = 2(2.5) / n

n = 5, 5th harmonic

I included parts (a) and (b) to show that I did think about this problem, I just got stuck with C. any help would be appreciated