First, remember that each particle in the medium experiences simple harmonic motion, so you can apply the SHM equations.

You should be familiar with all the pieces of the wave equation:
y(x,t) = A sin (kx ± ωt + φ)

Don't forget these other important topics:

• Superposition - the net displacement when there are multiple waves is the sum of the individual displacements.
  
  
• Interference - for two identical sources the path difference is key to determining what kind of interference, constructive or destructive, will result
  
  
• Musical instruments - the resonance frequencies are integer multiples of the fundamental frequency. You should know what the standing waves look like.