A wave is a disturbance which moves along a medium from one end to the other. If one watches an ocean wave moving along the medium (the ocean water), one can observe that the crest of the wave is moving from one location to another over a given interval of time. The crest is observed to cover distance. The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form,
If the crest of an ocean wave moves a distance of 20 meters in 5 seconds, then the speed of the ocean wave is 4 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 5 seconds (the same amount of time), then the speed of this ocean wave is 5 m/s. The faster wave travels a greater distance in the same amount of time.
Sometimes a wave encounters the end of a medium and the presence of a different medium. For example, a wave introduced by a person into one end of a slinky will travel through the slinky and eventually reach the end of the slinky and the presence of the hand of a second person. One behavior which waves undergo at the end of a medium is reflection. The wave will reflect or bounce off the person's hand. When a wave undergoes reflection, it remains within the medium and merely reverses its direction of travel. In the case of a slinky wave, the disturbance can be seen traveling back to the original end. A slinky wave which travels to the end of a slinky and back has doubled its distance. That is, by reflecting back to the original location, the wave has traveled a distance which is equal to twice the length of the slinky.
Reflection phenomenon are commonly observed
with sound waves. 
When
you let out a holler within a canyon, you often hear the echo of
the holler. The sound wave travels through the medium (air in this case),
reflects off the canyon wall and returns to its origin (you); the result
is that you hear the echo (the reflected sound wave) of your holler. A
classic physics problem goes like this:
In this instance, the sound wave travels 340 meters in 1 second, so the speed of the wave is 340 m/s. Remember, when there is a reflection, the wave doubles its distance. In other words, the distance traveled by the sound wave in 1 second is equivalent to the 170 meters down to the canyon wall plus the 170 meters back from the canyon wall.
What variables effect the speed at which a wave travels through a medium? Does the frequency or wavelength of the wave effect its speed? Does the amplitude of the wave effect its speed? Or are other variables such as the mass density of the medium or the elasticity of the medium responsible for effecting the speed of the wave? These questions were investigated in the Speed of a Standing Wave Lab performed in class. A wave generator was used to produce several waves within a rope of a measurable tension. The wavelength, frequency and speed were determined. Then the frequency of vibration of the generator was systematically changed to investigate the effect of frequency upon wave speed. Finally, the tension of the rope was altered to investigate the effect of tension upon wave speed. Sample data for the experiment are shown below.
Speed of a Standing Wave Lab - Sample Data
(N) |
(Hz) |
(m) |
(m/s) |
|
In the first five trials, the tension of the rope was held constant and the frequency was systematically changed. The data in rows 1-5 of the table above demonstrate that a change in the frequency of a wave does not effect the speed of the wave. The speed remained a near constant value of approximately 16.2 m/s. The small variations in the values for the speed were the result of experimental error, rather than a demonstration of some physical law. The data convincingly show that wave frequency does not effect wave speed.
The last three trials involved the same procedure with a different rope tension. Observe that the speed of the waves in rows 6-8 are distinctly different than the speed of the wave in rows 1-5. The obvious cause of this difference is the alteration of the tension of the rope. The speed of the waves was significantly faster at higher tensions. So while the frequency did not effect the speed of the wave, the tension in the medium (the rope) did.
A similar study was conducted in the Exploring Waves Simulation conducted in class. In this simulation, various properties of a wave (frequency, wavelength, and amplitude) were systematically altered to see if they effected the wave speed. Then various properties of the medium (mass density, spring constant, and damping coefficient) through which the wave traveled were altered to see if they effected the wave speed. The outcome of the study revealed that the speed of a wave was not dependent (causally effected by) the properties of the wave; rather the speed of the wave was dependent upon the properties of the medium.
One theme of this unit has been that "a wave is a disturbance moving through a medium." There are two distinct objects in this phrase - the "wave" and the "medium." The medium could be water, air, or a slinky. These media are distinguished by their properties - the material they are made of and the physical properties of that material such as the density, the temperature, the elasticity, etc. Such physical properties describe the material itself, not the wave. On the other hand, waves are distinguished from each other by their properties - amplitude, wavelength, frequency, etc. These properties describe the wave, not the material through which the wave is moving. The lesson of the Exploring Waves Simulation and the Speed of a Standing Wave Lab is that wave speed depends upon the medium through which the wave is moving. Only an alteration in the properties of the medium will cause a change in the speed.
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