Matthew Mehrkens –
Benjamin Rorem –
Thomas Huber –
Gustavus Adolphus College
Department of Physics
800 West College Avenue
Saint Peter, MN 56082

Popular version of paper 1pUW4, “Videos of ultrasonic wave propagation through transparent acrylic objects in water for introductory physics courses produced using refracto-vibrometry”
Presented Monday afternoon, May 7, 2018, 2:30pm – 2:45pm, Greenway B
175th ASA Meeting, Minneapolis

In most introductory physics courses, there are units on sound waves and optics. These may include readings, computer simulations, and lab experiments where properties such as reflection and refraction of light are studied. Similarly, students may study how an object, such as an airplane, traveling faster than the speed of sound can produce a Mach cone. Equations, such as Snell’s Law of Refraction or the Mach angle equation are derived or presented that allow students to perform calculations. However, there is an important piece that is missing for some students – they are not able to actually see the sound or light waves traveling.

The goal of this project was to produce videos of ultrasonic wave propagation through a transparent acrylic sample that could be incorporated into introductory high-school and college physics courses. Students can observe and quantitatively study wave phenomena such as reflection, refraction and Mach cone formation. By using rulers, protractors, and simple equations, students can use these videos to determine the velocity of sound in water and acrylic.

Video that demonstrates ultrasonic waves propagating in acrylic samples measured using refracto-vibrometry.

To produce these videos, an optical technique called refracto-vibrometry was used. As shown in Figure 1, the laser from a scanning laser Doppler vibrometer was directed through a water-filled tank at a retroreflective surface.


Figure 1: (a) front view, and (b) top view. The pulse from an ultrasound transducer passes through water and is incident on a transparent rectangular target. To measure propagating wave fronts using refracto-vibrometery, the laser from the vibrometer traveled through the water and was reflected off a retro reflector.


The vibrometer detected the density changes as the ultrasound wave pulse passed through the laser beam. This process of measuring the ultrasound arrival time was performed thousands of times when the laser was directed at a large collection of scan points. These data sets were used to create videos of the propagating ultrasound.

In one measurement, a transparent rectangular acrylic block, tilted at an angle, was placed in the water tank. Figure 2 is a single frame from a video showing the traveling ultrasonic waves emitted from a transducer and reflected/refracted by the block. By using the video, along with a ruler and protractor, students can determine the speed of sound in the water and acrylic block.

Video showing ultrasonic waves traveling through water as they are reflected and refracted by a transparent acrylic block.

Figure 2: Ultrasonic wave pulses (cyan and red colored bands) as they travel from water into the acrylic block (the region outlined in magenta). The path of the maximum position of the waves are shown by the green and blue dots.

In a similar measurement, a transparent acrylic cylinder was suspended in the water tank by fine monofilament string.  As an ultrasonic pulse traveled in the cylinder, it created a small bulge in the surface. Because this bulge in the acrylic cylinder traveled faster than the speed of sound in water, it produced a Mach cone that can be seen in the video and in Figure 3.  Students can determine the speed of sound in the cylinder by measuring the angle of this cone.

Figure 3: Mach cone produced by ultrasonic waves traveling faster in acrylic cylinder than in water.

Video showing formation of a Mach cone resulting from ultrasonic waves traveling faster through an acrylic cylinder than in water.

By interacting with these videos, students should be able to gain a better understanding of wave behavior. The videos are available for download from

This material is based upon work supported by the National Science Foundation under Grant Numbers 1300591 and 1635456. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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