Resource Lesson
Vibration Graphs
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A
vibration graph
displays the behavior at a SINGLE location along the wave's path as time passes. One
vibration
can be defined as one complete cycle, or back and forth motion.
The
period of a periodic wave
is defined as the amount of time required for a vibrating particle to return to its original observed position. The period can be calculated using the following equation:
When calculated, the
unit of measure is usually expressed as just seconds (sec)
, instead of seconds per vibration. But either are considered to be correct.
The
frequency of a periodic wave
represents how many vibrations a particle makes in a given amount of time, usually one second. It can be defined as
When calculated, the
unit of measure is usually expressed as hertz (hz)
, instead of vibrations per second. But either are considered to be correct.
As you can see from their respective definitions,
period and frequency are reciprocals
.
Remember that the
amplitude of the graph
is an indication of a mechanical wave's energy content; the greater the amplitude, the more energetic the source that produced the waves. We are now going to examine to vibration graphs in detail.
Refer to the following information for the next seven questions.
On this graph, the x-axis represents time in seconds.
At what time does the first recorded crest occur?
How many crests are displayed on the graph?
Based on the crests displayed on this graph, how many vibrations occurred?
At what time did the last crest occur?
What is the period of these vibrations?
Would you have gotten the same value for the period had you counted troughs instead of crests? Why or why not?
What was the frequency of the source producing these waves?
Refer to the following information for the next three questions.
On this graph the x-axis once again represents time in seconds.
Based on the number of crests, how many complete vibrations are displayed on this graph? You may assume that the first "indisputable" crest starts at approximately 2.1 seconds.
What was the frequency of the source that generated this wave?
Which source was more energetic: source A that generated the graph we just analyzed (in blue) or source B that generated the vibration graph shown below?
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