Test your function for g(x,t) here. g(x,t)=
(Note: To try your g(x,t) function, don't just hit the "Enter" key on your keyboard
-- click the "Enter" button on this page.)
What wave function g(x,t) (middle panel), when added to f(x,t) (top panel), will produce a beat wave with a beat frequency of 0.2 Hz? Note that the superposition of f(x,t) and g(x,t) will appear in the bottom panel. Experiment with various functions for g(x,t) by entering your function in the small textarea immediately below the simulation and then clicking the "Enter" button next to the textarea. If you aren't sure how to answer this question, please explain what you do know about producing beats. Also, feel free to "play" with changing different parameters in the equation for g(x,t) to help you understand what each parameter affects or represents.
(Simulation Hints! Click the "Forward" button to run the simulation.
The controls at the bottom work like VCR controls. You can click and drag inside
the animation to read the coordinates in order to obtain numerical values
for use in your equations. A running time display is in the top left corner
of the top panel. Also note that you may want to stop the animation
in order to measure things like the wavelength.)
Hints: Remember that a traveling wave y(x,t) can be described by y(x,t) = A sin (kx + wt), where y is the amplitude of the wave, k is the wavenumber ( = 2p/wavelength), x is the position in meters, w is the angular frequency ( = 2p/period), and t is the time in seconds. The speed of the wave is just the rate at which a certain point on the wave (e.g., a point of maximum amplitude) moves along, and is given by v = wavelength/period.