Two plots concerning a sinusoidal traveling wave on a wire are shown below. The

Question

Two plots concerning a sinusoidal traveling wave on a wire are shown below. The first plot is a snapshot (at a specific time) of the wire as a function of position from x=0 to x=2165 cm. The second plot is of the time dependence of a specific point on the wire from t=0 to t=0.3832 s. Pay attention to the units of the graphs, and note that the patterns you see repeats itself an integer number of times in each graph.

The general form of the wavefunction for this traveling wave is given by:

Find

Wavelength

Period

Frequency

Angular Frequency

Wave Number

Explanation / Answer

a) From first graph, the wavelength is the length of single wave (in cm). Pick a starting point on the wave, such a peak or a valley or a zero-crossing. Now move to the right and find the first place where that exact point occurs again. The wavelength is the horizontal distance between those points, expressed in the units of the graph. It is the distance over which the wave repeats itself.

                  Wavelength (L) = ~450 cm

b) Now do the same on the second graph to find the period of the wave. Note that the units are now in seconds. The period is the time over which the wave repeats itself.
                         Period (T) = ~0.05 sec

c) The frequency is just the inverse of the period.

                       f = 1/T = 20 Hz

d) Angular frequency = w = 2pi*f = 2pi*20 = 125.66 rad/s

e) Wave Number = k = 2pi/L = 0.014 cm^-1

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