Dependence of frequency on length. Hold the first turn of your slinky in your left hand and the last turn in your right, with your hands about 3 feet apart. Measure the frequency for vertical oscillations. (Don't worry about the sag.) Next stretch the slinky out as far as you can reach. Measure the frequency. Now fasten each end to something so that the total length is 8 or 10 feet. Measure the frequency. Explain your result. Use your frequency measurement to determine the inverse spring constant per turn. Suppose that N is the total number of turns of the slinky. Hold or fasten the slinky so that only M turns are free. (M < N.) Before doing the experiment, predict the frequency dependence on M/N. Then do the experiment.

Slinky as a continuous system. Fasten each end of the slinky to something fixed. A convenient length is 8 to 10 feet. (Don't worry about the sag.) Excite the lowest transverse mode in each transverse direction. Measure the frequencies for both modes. Next learn how to excite the second mode, in which the length L is two half-wavelengths. Measure the frequencies of the transverse modes. With some practice you should be able to excite the third mode.

Phase velocity for waves on a slinky. The phase velocity v was introduced in describing traveling waves. It satisfies v = λν. We also know what λ and ν mean for standing waves; therefore we can find v by studying standing waves instead of traveling waves. Send a short "pulse" or "wave packet" along the slinky to measure v. Compare it to value you determine from the standing wave frequency.

Transitory Standing Waves . Attach one end of a slinky to a telephone pole or something. Hold the other end. Stretch the slinky out to 30 feet or so. Shake the end of the slinky about 3 or 4 times as rapidly as you can. Watch the waves travel back and forth. Shake the slinky again, this time keeping your attention fixed on a region near the fixed end of the slinky. As the waves come in, reflect, and return, you should see a transitory standing wave during the time interval in which the incident and reflected waves overlap. That should help convince you that a standing wave can always be regarded as the superposition of two traveling waves traveling in opposite directions.