There's a lot to keep straight the first time you see simple harmonic motion. Remember the formula x(t) = Acos(ω t + φ) deals with radians in the cosine—ω is angular frequency, not frequency. Questions will often ask you to convert between the two.
Waves
Be careful with the formula for wavelength (v = fλ). It relates the speed of a wave and its frequency f—not its angular frequency ω.
Standing Waves and Interference
When figuring out the wave that results from two interfering waves, make sure to add the amplitudes at the correct points on the wave—if the frequencies or wavelengths don't match, you can't just add crests and troughs.
The Doppler Effect
Remember that the true frequency of the wave doesn't change in a Doppler situation. If the observer travels next to the object emitting the sound (say you're driving along beside the fire truck—or riding in it), the wave will never change.