Simple Harmonic Motion in stratified fluids- Dancing Test Tubes Experiment

  • Conduct a hands-on laboratory activity (Dancing Test Tubes) to demonstrate simple harmonic oscillation in a stratified fluid.
  • Use this suggested activity to allow your students to visualize how a parcel of water/air can perform SHM in the presence of a density gradient.

Use this suggested activity to visualize how a parcel of water/air can perform SHM in the presence of a density gradient. This laboratory activity or 'Dancing Test Tubes Experiment' is useful to demonstrate Simple Harmonic Motion in stratified fluids.

  • Take a large beaker (volume ~4 liters).
  • Fill it with 2 liters of regular water.
  • Prepare a saturated salt solution by dissolving ~0.5 kg of table salt in another container with 2 liters of regular water.
  • Dip a glass rod into the beaker.
  • Pour the saturated salt solution along the glass rod into the beaker. This is done so that the salt solution reaches the bottom of the beaker with minimal mixing with the regular water
  • Now the beaker contains the heavier salty water at the bottom and the lighter regular water at the top.
  • Fill 2-3 test tubes with regular water. Leave ~10% of the test tube volume unfilled.
  • Invert the test tubes and insert them into the large beaker. They should sink to the bottom of the beaker. They should also have a small air bubble.
  • Adjust the unfilled amounts in the test tubes so that all the test tubes do not sink to the bottom.
  • Heat the beaker using a hot plate.
  • After some time, the test tubes start oscillating within the beaker.

Classroom discussion for teachers and students:

  • Ask your students to recall Archimedes' principle of buoyancy of fluids- the force acting on an object immersed in water is equal to the weight of the water displaced by the object. Explain to the students that this principle works in any fluid -air, water, and lava.
  • Ask students how the weight of water can be changed by adding salts, by heating/cooling. Explain that as ocean water is saltier at the bottom than at the top, it is heavier at the deeper levels than near the surface of the oceans.
  • Therefore, if you move a small 'parcel' of water to the top from the bottom it will be heavier and sink. Similarly, if you move a parcel of water from the top to the bottom, it will be lighter and rise.

Archimedes principle of buoyancy of fluids

  • Explain that this sets the stage for simple harmonic motion -a force that is always acting in the opposite direction of the displacement.
  • Remind the students that initially in the lab activity, the test tube filled with regular water is heavy enough to sink to the bottom. As the beaker is heated, the test tube also gets heated and the air expands just enough to make them lighter than the salty water around them. The test tube then rises until it reaches the regular water near the top. The test tube is now denser than the water surrounding it, and it starts sinking.
  • Explain to your students that the test tubes represent water or air 'parcels' in the ocean and atmosphere. In this experiment, the test tubes are displaced by heating the beaker and they begin to oscillate. This is analogous to the displacement of water or air parcels in Earth's oceans and the atmosphere.
  • Discuss how such a displacement can generate internal waves that result in the redistribution of energy within these systems.