Lesson 36 SUPERPOSITION AND INTERFERENCE

1)

The Physlet to the left shows the amplitude of the function f(t) as a function of time. The portion of the wave that falls between the two vertical red lines in the top panel is "blown up" in the middle panel. You can tell from looking at the form of f(t) that it is the sum of two distinct sine waves, corresponding to two distinct tones or musical pitches. What you hear is the wave that results from the superposition or sum of those two distinct waves. Which of the following examples produces a beat wave with the greatest beat frequency? Please explain how you can tell, and please also explain what determines the beat frequency you get when you add two waves together. Note: Feel free to "play around" with other f(t) functions! Just type your function into the textbox [following the format you see in the f(t) textbox originally] and click the "New" button. You can turn the sound on/off by checking or unchecking the "Mute" option. Have fun! Beats, Example 1 Beats, Example 2 Beats, Example 3 Beats, Example 4 Beats, Example 5 Beats, Example 6

2) Be sure the simulation has finished loading before you begin.

Test your function for g(x,t) here. g(x,t)= 1*sin(1.5*pi*x+2*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.

3) Two identical pulses travel toward eachother on a string. At the instant they overlap completely, the displacement of the string is

1. exactly zero.
2. Half the amplitude of one of the pulses.
3. equal to the amplitude of one of the pulses.
4. twice the amplitude of one of the pulses.

You may change your mind as often as you wish. When you are satisfied with your responses click the SUBMIT button.

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