Waves An Interactive Tutorial (Forinash and Christian)

This is a set of interactive tutorials designed to teach the fundamentals of wave dynamics. It starts with very simple wave properties and ends with an examination of nonlinear wave behavior. The emphasis here is on the properties of waves which are difficult to illustrate in a static textbook figure. The tutorial may be used in conjunction with a text or as a stand alone introduction to waves. Exposure to calculus and basic physics is assumed in the latter sections.

Resonance is defined to occur when a vibrating system is driven with a frequency that causes the largest amplitude. Generally this occurs when the driving frequency equals the natural frequency. An example of resonance is when a wine glass is driven by sound waves with a frequency equal to the natural frequency of the glass. If the amplitude becomes large enough the glass will break. There are many other examples of resonance. Musical instruments depend on the phenomena of resonance to produce fixed pitches, tuning a radio to a particular chanel depends on selecting a resonance frequency and Magnetic Resonance Imagining (MRI) in the medical world uses resonance to form images of the inside of the human body.

Longitudinal Waves

In comparing simulations on transverse waves (Tutorial 1.3) with vertical harmonic motion (Tutorial 1.4) we discovered that particles in a transverse wave move up with simple harmonic motion. In the previous exercise (Tutorial 1.5) we saw that harmonic motion can also occur in the horizontal direction. Can we also have a wave moving horizontally where the particles move with harmonic motion in the horizontal direction?

YES! Longitudinal waves are waves where the motion of the material in the wave is back and forth in the same direction that the wave moves. Sound waves (in air and in solids) are examples of longitudinal waves. When a tuning fork or stereo speaker vibrates it moves back and forth creating regions of compressed air (where the pressure is slightly higher) and regions in between where the air has a lower pressure (called a rarefaction). These compressions and rarefactions move out away from the tuning fork or speaker at the speed of sound. When they reach your ear they cause your eardrum to vibrate, sending signals through the rest of the ear to the brain.

The following simulation shows a graph of the longitudinal motion of one molecule, the red circle, in a collection of molecules which has a longitudinal wave passing through it, much like sound passing through air. A vertical line marks the equilibrium location of the red circle. Random thermal motions are not shown.