Transverse Waves: The wave machine is a very simple device used to show what transverse waves look like. It has many long steel rods connected by a thin wire. When you move the rod on the end, it transmits energy to the other rods through the wire.
This wave is also similar to the wave you do at sporting events. Instead of people moving up and down, we have metal rods moving up and down. In both cases, energy is transmitted in the form of a wave. A sound wave is similar to this, but in a sound wave the movement is back and forth instead of up and down.
Longitudinal Waves: To show how longitudinal waves work, we use the slinky demonstration shown in the video below. A metronome at one end of the device pushes and pulls the end of the slinky at a constant frequency. The speed at which waves (both light and sound) travel is dictated by the medium in which they are propagating. Therefore, the speed with which the wave travels down the slinky is a property of the slinky, however the frequency and wavelength of the waves can be modulated by the metronome.
The wave shown here is analogous to a sound wave and we can use it to see what different frequencies look like. As sound travels through air, the wave creates zones of high pressure and low pressure as it moves along. The sound wave eventually makes its way to our heads where the pressure differentials vibrate our eardrums. These vibrations are interpreted by our brains as sound!