A Demonstration Measurement of the Speed of Sound
This method was first published as "A Visual Measurement of the Speed of Sound," L. M. Winters, The Physics Teacher 31, 284 (1993).
Equipment and techniques are described for measuring the speed of sound in a classroom demonstration using two sound triggers, two electronic flash units, a stroboscope, and a fan motor converted for use as a high-frequency clock. By separating the two triggers and producing a loud sound near one of them, a time delay results between discharges of the flash units. This delay is measured by using the high-speed clock. Visual estimates of the angle are sufficient to determine a value of the speed of sound to within 10%.
The accuracy of the method is not as important as the fact that students can see for themselves how the method works and how short time intervals are measured. The time-keeping technique is one they're already familiar with from reading analog wall clocks (clocks with hands). This activity will reinforce the fact that analog clocks measure time in terms of angle. The students will use proportional reasoning in order to apply this knowledge to the high-frequency analog clock used in the speed of sound measurement. Since ratio and proportion are required for the calculation of the speed of the sound, this part of the activity is limited to middle-school and higher grades. However, younger students can benefit simply from seeing that sound takes time to travel, even over short distances.
Since some of the equipment is described elsewhere on this site, relevant links are provided in order to avoid duplicating that material here.
Equipment and method notes
On the high-frequency clock: The calculations of the speed of sound work best if the clock has a frequency of 50 rotations per second (within 1 rps). The frequency of the clock can be adjusted prior to the demonstration by trimming the diameter of the clock disc. Follow the link given previously for a description of the method.
Control of flash duration: It must be possible to minimize the duration of each flash discharge so that the images of the clock hand will be sharp. This can be done by setting the flash unit on automatic exposure. Or, if the flash unit has variable power settings, use the lowest power setting. If your flash has neither automatic or variable power control, you will not be able to use it for this demonstration. (more information on controlling flash duration)
Setup and testing: Refer to the diagram below for the arrangement of the apparatus used in doing the demonstration. (Electrical connections are not shown.) The sound is produced to one side of one of the sound triggers at a point in line with both triggers. In that way, the distance traveled by the sound between flash discharges is just the separation of the triggers. When you clap the blocks together, you should see two images of the hand on the clock disc. As you vary the separation of the triggers, the angle between the images should change proportional to the separation of the triggers. You may occasionally get significantly larger separations than expected. This seems to happen when the sound from the blocks isn't loud enough.
Wooden blocks work well for producing a sound with frequency components to which the triggers are most sensitive. A loud sound seems to work best. Perhaps any differences in the electrical responses of the two triggers are minimized by using loud sounds. If the demonstration is performed in a small, live room, echos may cause multiple flash discharges. If the room is filled with people, that helps since people are good sound absorbers. (The term live is used here to mean highly-reflective of sound.)
Test the sound triggers for equal response by placing them next to each other and clapping the blocks above them. Watch the disc as you do. The two images of the hand should overlap. (An angle of 5° or less between images of the clock hand would indicate a time interval of less than 0.3 ms, an acceptable difference for the demonstration.) If there's a significant separation, you'll need to adjust the sensitivity of one of the triggers to given them equal response. You'll first need to determine which flash goes off first. (This can be done by placing colored filters over the flash units to mark them and noting which way the disc turns.) Then increase the sensitivity of the slow trigger or decrease the sensitivity of the fast trigger.
If you make repeated checks, be sure to allow the flash units to recharge between checks. If not fully charged, the discharge may be delayed slightly.
During the demonstration, it is recommended that the triggers be placed far enough apart to give an angle of about 90°, since that angle is easy to estimate visually. For a 50 rps motor, the separation of the microphones would be expected to be about 1.7 m. (In actuality, it is typically a little less, since the far microphone may not respond as readily to the lower intensity of sound that reaches it.)
A 100 kb video clip shows the appearance of the disc when the flash units discharge. Red and blue filters were used on the flash units.
The demonstration works well for both middle-school and high-school students, but the approach may be different for the two age groups. High-school physics students might be asked to predict how far apart the triggers should be placed in order to yield an angular separation of 90°, given the clock frequency and the speed of sound. For middle-school students, it might work better to determine the trigger placements by trial and error, soliciting ample verbal direction from the students. The speed of sound could then be calculated.
Especially for middle-school students or students with weak math skills:
One advantage of using a 50 rps motor and an angle of 90° is that students who have anxiety about dealing with fractions may have an easier time of understanding the math. It is easy to see visually that 90° is 1/4 of a full rotation. It is not quite so easy for some students to recognize that the time for one rotation is 1/50 s. However, it may make sense if they think of the clock as dividing a second into 50 equal parts. Understanding this, it is one more step to realize that the time to rotate through 90° is 1/4 of 1/50 s or 1/200 s. Some students will quickly decide to multiply the two fractions; others will need to be led.
Calculating the speed, given distance and time, requires division by a fraction. Sense can be made of this by pointing out to the students what the demonstration has shown--that sound traveled the distance between the triggers, say, 1.6 m, in 1/200 s. How far, then, would the sound travel in 1 s, 200 times as much?
Something for all students:
Students are intrigued by the use of an electronic stroboscope to "stop" the clock disc. Spend some time on this. Have the students explain to you how the stroboscope measures frequency. There are always students who are eager to do this.
Sources of Error
After you've spent some time with this demonstration, you will find that you can easily get 10° variations in angles for the same trigger separation. (Some typical results are given below.) Moreover, the measured speed of sound is typically less than the expected value by 10 - 15%, on the average. While the demonstration is effective even with these errors, having to explain where they come from may be a challenge. This could be a good discussion question for students that are experienced in looking for sources of error. They may even be able to suggest ways to reduce the error.
Possible Places in a Physics (Physical Science) Course
If the purpose for this demonstration is to help students understand how fast sound travels, then it would logically fit into a unit on sound. If, however, the purpose is to show a method of measuring small time intervals and high speeds, it would make an interesting addition to a beginning of the year discussion of time and distance measurement. It could even be a first day activity, since prior knowledge of physics is not assumed.
These results were obtained from measurements taken from photographs of the clock disc. The expected value for the speed of sound was 345 m/s. Note that all but one of the 8 measurements gives a value less than the expected one. This might be because the trigger furthest from the source of sound responds a little slower due to the lower intensity of sound reaching it. This would result in a greater angle and a lower calculated speed. A difference in response time of about half a millisecond would account for the error.
Distance between microphones = 1.70 m
Frequency of motor = 49.5 rps