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Purpose: To demonstrate the propagation of compressional waves (P waves) and shear waves (S waves).
Supplies: Slinky
Background and Demonstration:
Seismic waves are used in locating and modeling earthquakes and underground nuclear explosions, and for imaging the interior structure of the Earth. In any solid material, there will be two elastic waves: the P (primary or compressional) wave and the S (secondary or shear) wave. While you are talking, your students are listening to P waves in a fluid (sound waves in air).
To demonstrate the propagation of P waves, have a helper hold one end of a stretched out slinky. Give the slinky a push along its axis; the spring will compress and dilate as the compressional or longitudinal wave travels along the slinky. The speed of the wave is related to the spring's resistance to being compressed (its incompressibility). Ask the students to concentrate on a particular section of the slinky (any section will do) so they can see the spring compress and dilate.
Demonstrating S waves is similar, except now you generate the wave by moving one end of the slinky in an up-down fashion. If the students concentrate on a particular portion of the slinky, they will see that that part goes up and down as the wave passes perpendicular to it. This is a shear (or transverse) wave. In this case the speed of the wave is related to the spring's resistance to being sheared (its rigidity). You can also illustrate the concept of shear deformation with the slinky in its original, unstretched shape. Ordinarily it has the shape of a cylinder, or if viewed from the side, a rectangle. Holding this cylinder vertically, with one hand on the top and one on the bottom, move the top part horizontally. The individual coils of the slinky will move progressively to the side, much like a deck of cards. Note that from the side the shape is changed to a rhombus, although the area (actually the volume of the cylinder) is unchanged. Shear deformation involves a change of shape with no volume change. To illustrate the rigidity of the slinky, let go of the sheared slinky; it snaps back into its original shape.
Theory:
If the incompressibility is k, the rigidity is mu, and the density is rho, the P-wave velocity in a solid, elastic material is VP = sqrt [(k + [4/3] mu) / rho] and the S-wave velocity is VS = sqrt [ mu / rho]. In a fluid (such as air, water, or the Earth's outer core), mu = 0, so VP = sqrt [k / rho] and VS = 0.
Since the slinky is really just a coiled wire, both P and S waves in the slinky occur by bending these coils. Thus, the incompressibility and rigidity of the slinky are directly related to the resistance of these coils being bent. This means that, unlike the solid materials of the Earth, P waves and S waves in a slinky will probably travel at similar speeds. You don't have to mention this for the purposes of the demonstration, though.
Jeffrey S. Barker (SUNY Binghamton) Demonstrations of Geophysical Principles Applicable to the Properties and Processes of the Earth's Interior, NE Section GSA Meeting, Binghamton, NY, March 28-30, 1994.
Questions or comments: jbarker@binghamton.edu
Last modified: March 18, 1996 (content), June 6, 2021 (reformatted and moved to Google sites)
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