PHYS-302, Physics of Waves (Summer 2007)

W9 - Interference (Chapter 11)

Topical Outline for two-hour class:

Constructive and Destructive Interference - we used superposition to add two waves with the same frequency and amplitude but different phases and found that the resulting wave has an amplitude that depends on the phase difference between the two waves.
Phase Differences - we discussed the two principle ways of generating phase differences: (i) reflections from a boundary (hard or soft), and (ii) differences in path lengths from two coherent sources.
Path Length Differences - .
Young's Double Slit Experiment - we discussed Young's Double Slit experiment and found that the distance between 'bright fringes' (constructive interference) is where lambda is the wavelength, D is the perpendicular distance from the sources to the plane where the fringe pattern is being observed and d is the separation distance between the sources.
Hands-on Activity - We looked at three examples of pathlength dependent interference (double slit): monochromatic light waves passing through a double slit, water waves from two point sources in a Ripple Tank, and sound waves from two widely spaced loudspeakers driven by the same function generator. Here's the spreadsheet with student data and Dr. Russell's comments.

Hands-on Activities

Young's Double Slit Experiment with Laser Light (632nm)

Three students (who hadn't already done the double slit experiment in Modern Physics or Optics) measured the distance between bright fringes (constructive interference) as a function of distance D to the screen. The students observed that as the distance between the slits and the screen decreased, the spacing between bright fringes also decreased, just as theory predicts. The light source was monochromatic light from a helium-neon laser with a wavelength of 632 nm, and the double slits were separated by 0.25mm. This means that a plot of delta-y versus D should have a slope of 2.528e-3. The plot at right shows that the students obtained a slope of 2.1e-3.

Two Point Sources in a Ripple Tank

Another group of students observed the interference pattern for two points sources in a Ripple Tank. They kept the frequency of the waves constant (wavelength = 1.6cm) and measured the distance between regions of destructive interference at a distance of 32cm from the sources. They observed that as the source separation increased, the distance between destructive regions decreased, as expected. They made a plot of delta-y versus 1/d and found the slope of the line to be 48.7 compared to an expected value of 51.2.

Students measuring the distance between interference fringes with a Ripple Tank

Interference pattern for the Ripple Tank

The same intereference pattern with the regions of destructive interference identified by the black lines.

Interfernce from two loudspeakers

Third group of students tried to observe interference patterns from two loudspeakers. Two identical loudspeakers were driven with a frequency of 1000 Hz from the same function generator. The speakers were 2.16 m apart, and the students used sound level meters to measure the loudness of the combined sound waves at a distance of 4.6 m. This should have resulted in a spacing of about 72 cm between loud (constructive interference) regions. However when we tried it in the classroom, the presence of tables and chairs, and the hard floor and walls made prevented the experiment from working well. The students were able to find some places where the sound was noticeably louder (10 dB) than quiet regions, but the separation between loud locations was about half of what the theory predicted.

We tried moving the tables and chairs out of the way, and while it made the detection of loud and quite regions a bit easier to detect, it didn't significantly improve the quality of the data.

NOTE: When Dr. Russell tried it before class in the acoustics lab - which has carpet on the floor and absorbing material on the walls, and a big open space - it worked rather well. However, because of the large wavelengths associated with sound waves, and the problem of reflections from surfaces and objects in a typical classroom room, this experiment would be better conducted either outdoors (grass is a good absorber reducing reflections) or in the acosutics lab.

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