Apparatus Competition

2006 AAPT Summer Meeting

Syracuse, NY

Surface Gravity Waves: Resonance in a Fish Tank

John J. Lynch

Department of Physics

Wheeling Jesuit University

316 Washington Ave.

Wheeling, WV 26003

304-243-2287

jlynch ‘at’ wju ‘dot’ edu

Abstract:

This apparatus is used to study wave motion using a 10-gallon glass aquarium. It is an alternative to vibrating strings and resonance tubes. The equipment needed is inexpensive and the resulting waves are much slower than those produced by string vibrators and tuning forks. Times can be measured with a stopwatch. In addition, students can study projectile motion with the squirt gun.

Construction of Apparatus:

10-gal Aquarium Tank

Stopwatch

Plastic ruler

Meter Stick

2 Styrofoam strips

Squirt gun

Water

Use of Apparatus:

(1) Fill the tank with water to the desired depth, D.

(2) Measure the inside length of the tank, L.

(3) Excite the fundamental resonant mode (n=1). The antinodes will be at the edges of the tank. Place the styrofoam strips at these edges and begin to move them up and down and out of phase. Let the water establish the tempo.

(4) Once a clear standing wave is visible, remove the strips and use the stopwatch to measure 20T--the time for twenty oscillations.

(5) Obtain the wavelength λ_n from

the condition for resonance.

(6) Calculate the wave speed using the wavelength and the period.

(7) Calculate the wave speed using the dispersion relation for surface gravity waves.

(8) Compare the two numbers from steps (5) and (6).

(9) Excite the next fundamental resonant mode (n=n+1). Place the Styrofoam strips where antinodes are expected to be and move them up and down in the water. Let the water establish the tempo. Return to step (3).