# Demonstration goals:

• Demonstrate the effects of on S-wave speed
• Demonstrate the effects of on S-wave speed
• Understand how these effects interact

#### IDEA:

When a string is plucked, it moves in the same manner as an S-wave traveling through the Earth; the string vibrates perpendicularly to the direction of wave motion. (The sound is carried to our ears by a compressional wave, since shear waves cannot travel through the air; this is a nice example of S- to P-wave conversion.) The pitch of the sound is proportional to the wave speed; thus, by using our ears and a rubber band, we can illustrate the effects of the shear modulus () and density () on S-wave speed ().

If we examine the equation for S-wave velocity (), we can make some predictions about what should happen, both in our model and in the Earth. As increases, the wave speed increases, whereas an increase in should lead to a decrease in wave speed. The pitch (f) of a string is related to the wave speed and the wavelength by . Since the wavelength of the string does not change, increasing the wave speed will increase the pitch and give a higher note.

The shear modulus of a string or a rubber band is equal to the tension. By increasing the tension, we increase the wave speed, and the pitch of the sound made when the string is plucked. If we increase the density of the string, we decrease the wave speed and the pitch of the sound. This is why strings for low notes are wrapped with wire; the extra mass of the wire lowers the note even on a taught wire.

Since we know that density also increases with depth in the Earth, we might expect S-wave speeds to decrease in the Earth's interior. In fact, the opposite happens, because the shear modulus increases more rapidly.

To demonstrate this effect, you will need:

• Plastic Sandwich box (Or similar rigid box)
• 2 Rubber bands (You may want to keep a spare handy, as well)
• 2 Paperclips
• Scissors

Before the demonstration
Pull the rubber bands around the sandwich box, so that they stretch across the open side. Write the equation for S-wave velocity () on the board.

1. Ask what the the terms of the equation mean. Point out that wave speed is related to pitch, and increasing the wave speed will increase the pitch.

2. Start with . "Tune" the rubber bands so that they have approximately the same pitch and pluck them several times to demonstrate it. Now pull one rubber band very taught, and pluck the rubber bands again. Note the higher note on the tighter rubber band.

2. Now let's show the effect of increasing . Place a single paper clip on the center of the tight rubber band. Pluck the rubber band again, and note the dramatically lower pitch. Place a second paper clip on the rubber band and note the further decrease in pitch.

For Discussion:

How do these effects relate to various layers in the Earth? Why would the presence of some melt create a Low Velocity Zone? Does this effect explain how bending a saw can change the note being played?

## Back to the demonstration page

• To Seth Stein's Homepage

## Related experiments:

• Wave propagation on a string
• Snell's Law
• Travel Time measurements