Wave speeds of P- and S-WavesAaron Bunch

Abstract

The example of seismic waves in earthquakes leads us to expect that longitudinal and transverse waves will have different wave speeds in a Slinky. Using video analysis software, the speeds of longitudinal and transverse waves were measured in a PASCO scientific double-length Slinky. The experiment found no difference in the range of wave speeds. This suggests that, in contrast to solid rock, the Slinky communicates the energy of a wave just as easily transversely as longitudinally.

Methods

A PASCO scientific double-length Slinky was stretched out on the lab floor between two lab stools (Fig. 3A). Parchment paper was placed underneath the Slinky to reduce friction. A two-meter stick was placed on the parchment paper next to the Slinky, a few inches away so that it would not interfere with a wave-pulse travelling down the Slinky. A web-cam was mounted on a mast approximately six feet above the Slinky (Fig. 3B). At this distance, approximately 2.5 meters of the Slinky length were in view of the web-cam. The web-cam was connected to a computer running Logger Pro video analysis software. This software precisely determines distances, times, velocities, and accelerations of objects by analyzing video recordings of their motion. The computer mouse was positioned on the lab bench in such a way that I could initiate the video capture, and then quickly be in position to send several wave pulses down the Slinky. The wave pulses were generated by hand. When sending longitudinal waves, care was taken to impart as little sideways motion as possible to the Slinky in order to avoid creating transverse waves in addition to longitudinal waves. In the captured video, the image of the two-meter stick was used to set the scale. Each wave pulse was captured by six or seven frames of video. In each frame, the leading edge of the wave pulse was marked with the cursor. From these marks, the Logger Pro software calculated the time, distance, and velocity of the wave.

Data and Results

The velocity of the wave pulses was recorded in six or seven successive frames of video as the wave pulse traversed the Slinky. The recorded velocities of the P-waves and the S-waves in each frame are presented in separate charts (Figs. 4A, 4B). Both the P-waves and the S-waves were found to have wave speeds between 4.34 and 5.22 m/s. The error bars in the charts indicate the uncertainty in the wave speed in each frame of the video. In each frame, the S-waves have an uncertainty in their velocity of ± 0.17 m/s. The P-waves have an uncertainty of ± 0.38 m/s. The greater uncertainty in the P-waves is due to the greater difficulty in locating their leading edge.

Experiment Discussion

The results of the experiment do not support the hypothesis that the two kinds of waves have different speeds in the Slinky. No difference in the range of wave speeds was found. If there is a small difference in wave speed in the Slinky, more exact experimental methods will be required to detect it. Any difference in the speed of longitudinal and transverse waves likely depends on the nature of the medium. In an earthquake, the energy of a wave is communicated through rock more easily longitudinally than transversely, and for this reason longitudinal waves travel faster through rock than transverse waves. In contrast to rock, the results of this experiment suggest that a Slinky communicates the energy of a wave just as easily transversely as longitudinally. For this reason, longitudinal and transverse waves have the same speed through the Slinky. It is expected that differences in wave speed between types of waves will vary by medium. Future experiments should explore these differences in various media.

Introduction

Earthquakes produce three different kinds of seismic waves (Fig. 1): P-waves, S-waves, and surface waves. P-waves are longitudinal waves, S-waves are transverse, and surface waves have the complicated dynamics of rolling waves on the surface of the ocean.

Conclusion

The experiment found no difference in the range of wave speeds between longitudinal and transverse waves through a Slinky.

Figure 3: Experimental Set-up. A) Slinky on lab floor next to two-meter stick. B) Web-cam attached to mast with view of Slinky on the floor.

A B

Range: 4.34 – 5.22 ± 0.38 m/s

Range: 4.22 – 5.41 ± 0.17 m/sThese three kinds of waves travel through the mantle and crust of the Earth at different speeds. P-waves are approximately 60% faster than S-waves, and this difference in wave speed allows seismologists to estimate the distance to the epicenter of an earthquake (Earth Observatory of Singapore, <http://www.earthobservatory.sg/faq-on-earth-sciences/why-do-p-waves-travel-faster-s-waves>). As the waves travel out from the epicenter, the P-waves race ahead of the S-waves. This gap between P- and S-waves grows as the waves get farther from the epicenter. A researcher some distance from the epicenter can determine the distance to the epicenter from the size of the gap between the arrival of the P-waves and the arrival of the S-waves (Fig. 2). This experiment investigates whether longitudinal and transverse waves will have different speeds in other media. It is expected that longitudinal and transverse waves in a two-meter length of Slinky will have measurably different wave speeds.

Figure 1: Two of the three types of seismic waves: P-waves and S-waves.(Source: http://w3.shorecrest.org/~Lisa_Peck/Physics/All_Projects/Biggie_Project/2010/meghan/meghan1/soundScience.html)

Figure 2: The gap between P-waves and S-waves as recorded on a seismograph.(Source: http://www.sciencepartnership.org/uploads/1/4/3/7/14376492/earthquake-1.pdf)

Figure 4: Results. Wave speed verses distance for A) P-waves and B) S-waves.

A

B