Motion of the pendulum is oscillatory. The pendulum bob rises while it swings to the right, then it falls, and again rises as it swings to the left. In a typical pendulum, like one in a grandfather clock's, this motion repeats over and over again. Another commonly observed oscillatory motion is the one caused by a spring or other elastic medium. When we drive our car over a bump, for example, the car oscillates vertically, especially if it has a "bad suspension". Or when we drop a ball onto a drum skin, the ball bounces up and down repeatedly. There are still other, less familiar, oscillatory motions in nature.
What is common to all oscillatory motions is that, after a time, the motion repeats itself. The characteristic time that it takes the motion to repeat, i.e. to make one full cycle is, called the period of oscillation. In most oscillations the value of the period depends directly on the parameters of the oscillator itself. For example, in the case of the (simple) pendulum the value of the period depends on the length of the pendulum.
The frequency of oscillation is the number of full oscillations in one time unit, say in a second. A pendulum that takes 0.5 seconds to make one full oscillation has a frequency of 1 oscillations per 0.5 seconds, or 2 oscillations per second. The commonly used unit for number of oscillations per second is Hertz. So, this same pendulum is said to have a frequency of 2 Hertz.
A third measure of oscillatory motion is the maximum distance of travel of the oscillator. This is called the amplitude of oscillation. In the case of the pendulum its amplitude is the maximum height that the bob rises to. In the case of a mass-spring oscillation amplitude it is the maximum compression (or stretch) distance. Notice that to compress a spring further and further, you need to force it harder and harder. Similarly, to make a swing go higher and higher, you need to give it larger and larger pushes. So, the amplitude of oscillations is related to the energy of its motion. The more the amplitude, the higher the oscillator's energy.
There are two other useful concepts that relate to most oscillators: damping and forcing. All oscillators that interact with other things around them lose energy. A pendulum bob that is pulled to the side and released swings a few times and then it comes to a stop (typically, its amplitude undergoes a continuous decay) because of air friction and in friction in its pivot. This decay of amplitude is called Damping. To make the pendulum swing continuously we need to supply it with repeated "pushes". This is called Forcing it. So, a forced oscillator can continue to oscillate so long as the forcing is supplied. It is interesting to note that forcing with different frequencies can have different results, even though the amount of the force may be held fixed. In fact, in most damped oscillators the maximum amplitude of oscillations is reached when the forcing frequency is chosen to be equal to the natural frequency of the oscillator. This condition is called resonance.
When an oscillation is transmitted in space, we call this a wave motion. More strictly, we say that a wave is a traveling disturbance. This disturbance affects its surroundings as it travels through it. In physics, waves are disturbances that carry energy and momentum. So, as a wave travels it affects things by giving them energy and momentum, typically, by making them move or oscillate. An example of this type of motion that we all have observed is the case of water waves. When a water wave travels on the surface of water it makes floaters (say leaves or branches floating on the water surface) go up and down. Another way that energy and momentum get transferred is when objects ( i.e. material bodies such as particles, balls, cars, etc.) interact with one another as they collide with each other.
It is important to note that as the water wave travels in a horizontal direction the floater just goes up and down vertically. That is to say, the wave does not move the floater with it in its direction of travel. This is very different from the collision of particles. When a billiard ball collides with a second one it transfers momentum and energy by making the second ball move in the same direction as the first one was moving. This unusual feature of interaction of a wave with material bodies remains the case even for the type of waves in which the direction of disturbance (oscillation) is the same as the direction of motion of the wave, as in sound waves. Water waves and other waves in which their oscillation direction is perpendicular to their travel direction are called transverse, while sound waves and other compression waves in which these directions are the same are called longitudinal. Another interesting aspect of waves that is worth noticing is that all that travels is the disturbance. In the case of water waves, for example, the water itself (droplet/molecule/atom) does not move with the wave. Similarly, in the sound wave the air molecules don't travel, just the sound does. Check out the applet on logitudinal and transverse waves by Professor Fu-Kwun Hwang.
Vibrations caused by a wave, just as a vibrations caused by an elastic medium (say, a spring), have an amplitude, a period, and a frequency. So, a wave is also characterized by its frequency (or period) and its amplitude. In addition, the speed of transmission of the vibration is another measure for the wave. Another way of taking this measure (speed of transmission) into account is to instead refer to the distance that the wave travels to produce a full cycle of its vibration. This distance is called wavelength. In the case of water waves, for example, the distance from one peak to the next (or one valley to the next) is one wavelength. Notice that this measure, i.e. the wavelength, then depends not only on the speed of propagation of the wave, but also on the period (or frequency) of the vibration.
Not only waves behave very differently than material objects in the context of transmission of momentum and energy, but they also interact with each other differently than material objects do. When two objects meet each other they collide. Two waves, on the other hand, do not interact at all and pass "through" each other as ghosts pass through ghosts. But in the region where the two passing waves overlap the effective disturbance becomes a net sum of the disturbances of the two waves. So, when a floater happens to be "at the wrong place at the wrong time", i.e. where the peaks of the two waves meet, it experiences a much larger up-down motion. But were it is lucky to be where the peak of one wave meets the valley of the other, then it does not move at all; as if there were no waves passing by. This addition of disturbance, which does not affect the original waves, is purely a wave phenomenon and is called interference. So, waves do not collide, they interfere.
Exercise: to see how two waves interfere, work with the applet: Wave Interference Try changing the wavelength of the waves and their amplitudes. One of the interesting results is when the two waves have the same amplitudes and almost the same wavelengths, but not quite.
Another wave characteristic that has no analog when it comes to travel of material objects is that when a wave reaches an obstacle (or an opening), with dimensions comparable to its wavelength, it bends around the obstacle (and about the opening). This second wave phenomena is called the diffraction effect. Check the applet on Wave Diffraction to see this works. Try changing the opening size to see how the effects of the diffraction sharpen up or get washed out.
Last Modified: September 10, 2007 malekis@union.edu