Lesson 36
Name: etp       Section: M1       Start Time: 9:47:28       Instructor: Dr Evelyn E_Patterson       Course: 110H      


Be sure the simulation has finished loading before you begin.
Standing waves on a string occur when two identical waves travel past each other in opposite directions. (This happens when a wave sent down the string from one end reflects at the other end and comes back again.) In the simulation, the wave in the top panel is described by f(x,t) and travels to the right. The wave g(x,t) in the middle panel is identical to f(x,t) except for its direction of travel, so it travels to the left. The superposition of f(x,t) and g(x,t) is just the sum of those two waves at every point, and that superposition is the standing wave shown in the bottom panel.

Let n represent the number of half-wavelengths that 'fit' onto the string. Click on a blue link to see the f(x,t) and g(x,t) that are added together to produce the standing wave pattern that has n antinodes.

This simulation is a lot like an actual experiment we can set up in the classroom (and will use for our lab). Click through the links to observe the different standing wave patterns that correspond to different 'modes' of vibration.

  • What stays the same from mode to mode?
  • What changes as you go from mode to mode?
    (Hint: Consider things like the speed, wavelength, frequency, and amplitude of the waves f(x,t) and g(x,t).)

In your own words, try to describe what is being done here in order to change from one mode of vibration to another.

2) Stringed instruments work by setting up standing wave patterns on strings of different lengths, tensions, and densities. Suppose the piano string for the "A" above middle C has a mass of about 3 grams and a length of about 40 cm. The frequency of this "A" should be 440 Hz. If the vibration mode that's set up when you play the "A" is the lowest possible mode, estimate the tension required in the string. (Please briefly explain your steps. If you aren't sure how to complete the estimate, please explain what you do know.)

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.

Below is a space for your thoughts, including general comments about today's assignment (what seemed impossible, what reading didn't make sense, what we should spend class time on, what was "cool", etc.):

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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