PHYS-302, Physics of Waves (Summer 2007)

M3 - Introduction to Waves

Topical Outline for two-hour class:

• What is a Wave? - We began by discussing a definition of a wave:

  A Wave is a disturbance or variation that transfers energy (and momentum) progressively from point to point in a medium, and that may take the form of an elastic deformation, or of a variation in pressure, electric and magnetic intensities, electric potential, or temperature.

  We looked at several animations of longitudinal, transverse, and surface mechanical waves as well as Electromagnetic waves. We discussed how the wave speed is a constant that depends on the type of wave and the properties (elastic and inertia) of the medium through which the wave is propagating. We used our mechanical wave machine to see how the wave speed slows down or speeds up when the medium changes (in this case the inertia of the medium changed).
• Wave Function f(x,t) - we discussed an animation that Dr. Russell created to compare the difference between the time oscillation associated with a single location in the medium while a wave passes through, and a snapshot of the wave amplitude as a function of position in the medium at a specific time. We talked about periods and wavelenghths and the important relationship between wavespeed, frequency, and wavelength.
• Hands-on Activity (Wave Speed) - students explored the speed of waves. Two groups measured the speed of sound by measuring and plotting the distance travelled versus propagation time for a sound pulse. They measured the speed of sound to be 346m/s which agrees very well for the value expected at the temperature of the lab. A third group played with a ripple tank and made measurements of wavelength and frequency to find the linear relationship between them in terms of the wave speed. Here's a spreadsheet with the student results and with Dr. Russell's summary.
• Wave Function and Wave Equation - we discussed the general form for a wave function and discussed the meaning and interpretation of the terms in the equation motion for waves.

Hands-on Activities

Two groups of four students each measured the speed of sound waves by measuring propagation time for the sound to travel a given distance. A single cycle of a square wave pulse (period = 0.001s) was fed to a speaker in a tube, and the response of a microphone a distance x away was captured on a digital oscilloscope. (NOTE: in the future both the pulse signal and the measurement of the propagation time from the oscilloscope trace will be accomplished with LabView. We don't have LabView on the computers in our classroom yet, so during this first offering of this course, we're borrowing standalone hardware from some of our other labs in order to see what kind of hands-on activities work). The students measured the propagation time for speaker-microphone distances of 10cm to 120cm and plotted the distance versus time from which the slope gave the speed of sound waves (spreadsheet). One group measured the speed of sound in air to be 349m/s and the other group obtained 346m/s. The speed of sound waves in air depends on temperature - this morning the temperature in the lab was about 76oF, which results in a speed of sound 346m/s, so the data came out pretty well.

The other two group of five students measured the speed of water waves using a Ripple Tank. They set the frequency of the driver which created traveling waves in the water. They used a strobe light with a frequency counter to "freeze" the traveling wave in place and measured the wavelength. Their plot of wavelength versus period (1 over frequency) resulted in a straight line whose slope represents the wave speed (spreadsheet).