Standing Wave on a Thin Rope: Analyzing Harmonics

[Faraz]

Homework Statement

A fellow student of mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=2.30mmcos[(6.98rad/m)x+(742rad/s)t]. Being more practical-minded, you measure the rope to have a length of 1.35 m and a mass of 3.38 grams. Assume that the ends of the rope are held fixed and that there is both this traveling wave and the reflected wave traveling in the opposite direction.
a)What is the wavefunction y(x,t) for the standing wave that is produced?
b)In which harmonic is the standing wave oscillating?

Homework Equations

y(x,t)=Acos(kx-ωt)-Acos(kx+ωt)

The Attempt at a Solution

a)4.6cos(6.98x)-cos(72t)
b)N=PI/2K=2PI

 

[Simon Bridge]

Great. How did you arrive at those answers snd what do they mean?