PURPOSE: To demonstrate the relationship between the phase velocity and
the group velocity of a wavepacket.
DESCRIPTION: Two transparencies contain a series of equally spaced
parallel lines. One transparency has a line spacing five percent smaller than the
other. Place one transparency stationary onto the overhead, as shown in the photo
above at left. Place the second transparency on top of the first and tilt it to
create a small angle. Observe an interfernce pattern between the two overlapping
transparencies, as shown above in the middle photo. The smaller the angle between
the two transparencies the better the effect.
Keeping the first transpareny stationary, slide the second transparency across the OHD projector. The group velocity is seen to move rapidly across the picture, as shown in the photo at right. The movement of the phase velocity (motion of each transparency) is much slower than the fast moving group velocity.
EQUIPMENT: Transparencies, overhead projector.
SETUP NOTES: None.
To make your own transparencies, here is a jpg file of the parallel
lines. To make your own demo, download this file and print it on your printer.
Next, use a copy machine to make a one 1:1 transparency. Lastly, adjust the
copy machine to zoom a 5% reduction, and make a second transparency. Now you have
the demo!
References:
Robert Katz, Group-Phase Velocity Demonstrator, AJP 21, 388-389 (1953).
Eric Mendoza, Storm at Sea - An Illustration of Group Velocity, AJP 22, 208-211 (1954).
P. T. Demos, Device for the Visual Presentation of Group Velocity, AJP 25, 383-384 (1957).
N. F. Barber, Phase Velocity and Group Velocity, AJP 27, 120 (1959).
J. Mawdsely, Demonstrating Phase Velocity and Group Velocity, AJP 37, 842-843 (1969).
John Coenraads, notes: Phase and group velocity, TPT 11, 36-37 (1973).
Updated by Jun Qi in 3/24/2000
