Properties of Traveling Waves

We will leave complex plane waves for Section 3 and look at the properties of real traveling waves.  The imaginary part of a complex plane wave is treated in the same manner as the real part.

  f(x,t) =

g(x,t) =

In the applet above you will see three plots: f(x,t), g(x,t) and the sum of these two functions.  The functions  f(x,t) and g(x,t) may be changed by typing in a valid formula in the text field and pressing the Change button.  The other buttons control the time evolution of the functions.  Note that the current time is displayed in the upper left corner and the coordinates are displayed upon left-clicking in one of the plots.

Simple real traveling waves may be cast in the form:

 

where A is the amplitude, k is the wave number, w is the angular frequency, f is the phase constant, lambda is the wavelength and f is the frequency.  For simplicity, the value of the phase angle phi in these exercises is zero.

Student Exercises:

  1. Change the wave functions to the following:  
    f(x,t) = 2*cos(2.2*pi*x-2.2*pi*t) and g(x,t) = 2*cos(2.6*pi*x-2.6*pi*t).  
    Notice the changes in the plots.  Measure the amplitudes, wavelengths and frequencies of f(x,t) and g(x,t)?  Compare these values to what you would expect given the formulas for f(x,t) and g(x,t).
  2. Set the default conditions for the page.  Measure the amplitudes, wavelengths and frequencies of f(x,t) and g(x,t)?  Write the equations for f(x,t) and g(x,t).
  3. The velocity v of the wave is given by v = w/k  = f * lambda .  For Exercises 1 and 2, what was the velocity in each case?  Click the Run button and verify what you calculate.

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