# Graphs of Periodic Data

Initial Publication Date: December 21, 2006

The composite solar cycle shown above as measure by several satellite based instruments is a classic example of periodic data, **see References for Frohlich and Lean below. {click each image to enlarge it}

Of particular interest for periodic data are the:
• amplitude, A;
• period, T;
• and frequency, f.

The example above shows that: the amplitude is the maximum displacement from the average displacement, the period is the time it takes for the signal to repeat the cycle, and the frequency and period are reciprocals of each other.

• The activity Graphing Sunspots is a good example of graphing periodic data.

When two or more periodic signals are compared then the phase of one signal relative to the other signals becomes important. In this example, the signal in dark blue is 90 degrees (pi/2 radians) ahead of the light gray signal.

There are also cyclic signals in space that are characterized by a wavelength. In this case the wavelength (the distance over which the cycle repeats) can be measured from the graph instead of the period. There are many example of this in the geosciences. Among these include: Ocean waves, seismic waves, waves in clouds, and waves in sand.

• Click on the GOES image at left to see cloud waves as viewed from space.
• Waves in sand are good examples of cyclic patterns in nature. Students close to sandy areas can collect their own data and determine the wavelength of the observed waves in sand.

References/Resources
• **Total Solar Irradiance (TSI) Composite Database compiled from many satellite TSI data 1978-present, by Claus Frohlich and Judith Lean NOAA NGDC ftp link
• Waves on the Internet is a site with eight interactive exercises to help students learn more about waves in nature.
• Simple Harmonic Motion at Hyperphysics is a good online tutorial/review related to periodic motion.