There are two types of wave.  Transverse waves and longitudinal waves.  Sound is a longitudinal wave of varying pressure and transverse waves can be used to create these, on a string for example.

The diagram above shows all the important parts of a transverse wave.  The amplitude of the wave shows how powerful it is and this translates into how loud it appears to us.

The wavelength of the wave is related to the frequency by the formula v = f where v is the speed of the sound wave (330 m/s in air).

The peaks and troughs of a wave are always in phase with each other.   This means the wave moves symmetrically.

Sound waves obey the laws of reflection.  This means that the angle a wave is incident on a surface with is the same as that with which it leaves.

Sound waves have intensity.  This is the energy per second passing through a unit area in the direction of travel.  For a point source, the intensity (I) at a distance (r) from the source is I = W/4r², where W is the power of the emitter.  So therefore for a point source, the intensity follows an inverse square law I = k/r², where k is a constant which can be calculated using W/4.

The Doppler effect is simply that as a source of constant frequency is approaching, the waves will be apparently compressed to the observer, giving an increase in pitch.  If the source is receding then the effect is reversed and the pitch appears to fall.  An example of this is when an ambulance goes past and the apparent frequency of the siren changes.