Exploratories

MECHANICAL SNAKE

Problem

How can you study waves in a slinky?

Materials

Slinky, heavy metal spring, chalk, stopwatch or timing device, meter stick.

Procedure

A. Comparing the velocity of pulses.

Generate pulses in a slinky stretched out on a floor by one person holding one end firm and another person giving this end a single quick jerk sideways and back. This is called a transverse pulse. A longitudinal pulse can be created by plucking the coils parallel to the length of the slinky or spring. Be careful not to stretch the slinky past the point where it will not return to its original shape. Don't let go of one end when the slinky is stretched which will result in an unrepairable tangle or injury to your partner.
Form laboratory groups of about three students per group and practice generating different shaped pulses. Measure the velocity of pulses with changed variables such as type of pulse, stretch of the coil, etc. Organize a data table showing the variables tested and all measured data used to determine the velocity of the pulses.

B. Reflection and superposition of wave forms.

1. With your partner holding the far end of the slinky firmly against the floor, create a sharp single-pulse disturbance in your stretched slinky. Note carefully the direction of displacement of the original incident and reflected pulses.
2. You and your partner can generate a disturbance from both ends of the slinky at the same time; note whether the pulses pass through each other or reflect from the collision.
3. Now generate equal sized pulses from each end and compare the maximum displacement when they meet with the original pulses. Use a piece of chalk or paper glider to measure these displacements.

C. Standing Waves

Use the small diameter coil springs instead of the slinky for this part. It can be done either with the spring moving sideways on the floor or vertically up in the air. With your partner holding the opposite end of the spring, generate a standing wave by moving the end steadily back and forth at an appropriate frequency. If you have difficulty
establishing it, your partner could try moving forward or backward. Note that at a proper frequency the spring will vibrate in one, two, three or more segments.
Sketch all the different standing wave patterns you were able to generate.

A node is a region of the standing wave where there is no motion. The distance between two nodes is one-half a wavelength. Conduct an experiment to find a relationship between the wavelength and frequency of various standing waves. Show all your measurements in a well organized data table. What can you conclude from your
experiment?

Summing Up

1. What effect, if any did a greater stretch have on wave speed in the slinky?

2. How does the speed of the longitudinal wave compare with that of the transverse for the same stretch?

3. How does a reflected pulse compare to the original incident pulse?

4. Do the pulses appear to pass through each other or do they "bounce back" from collision with another pulse? How can you verify your answer?

5. How does the maximum displacement where the pulses meet compare with the displacement of each pulse?

6. What happens to the wavelength as the frequency increases?

Teaching Strategies

Because this is an exploratory activity, encourage students to try to generate various kinds of pulses. Students should recognize that they need to measure distance and time to compare velocities of the various pulses. Hopefully they can organize their own data table
by now. Some students want to compare only the time it takes the pulse to travel the length of the slinky even if they stretch it out farther and cause the pulse to travel greater distances. It is advisable for these students to make their own discovery of this type of
error instead of prelabing this precaution. Students will be able to make better observations if they work in groups of at least three students. Be sure to warn the students to not overstretch the springs or release either end of a stretched slinky since this causes considerable tangling of the coils.

Sample Observations/Calculations

Expect data tables to include the following information: description of the variable, distance pulse traveled, time for pulse to travel indicated distance and pulse velocity. Students should show that longitudinal pulses travel faster than transverse pulses; as the stretch in the spring is increased, the velocity of the pulse increases and the shape of the
pulse has no effect on the velocity. If the students have tried other variables give them praise for their efforts.

If a pulse is reflected from a rigid support it will reflect along the slinky on the opposite side. However, if the pulse reflects from a junction attached to a rope or less rigid material than the slinky, the pulse will reflect on the same side of the slinky. This is analogous to light reflecting from the boundary-y from a less optically dense medium to one of greater optical density where there is a 180' phase shift. When light reflects from the boundary-y going from greater to lesser optically dense material there is no phase shift in the light wave. You can show by generating two pulses of different shapes that the pulses do not reflect but rather pass through each other. Where the pulses meet the lateral displacement (amplitude) is greater than the amplitude of either pulse.
When generating standing waves it should be seen that the wavelength and frequency are inversely proportional to each other. In fact, the product of the wavelength and frequency is equal to the velocity of the pulse.