Physics lab assignments
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macaulay.cuny.edu
Kent State University
Act II Lab 4
Lab 4 Measuring the speed of sound
The idea: By our standards, sound travels super fast, about the speed of a fast bullet. Even so, we can measure that speed in the lab. Today you will measure the speed of sound in two ways. The first takes advantage of the distance learning format and the wide open spaces outside a conventional laboratory (Part 1). The other is a clever indirect method (Part 2) that students use in the face-to-face version of this course.
What you’ll learn: By the end of this experiment you will understand 1) how to measure the speed of sound outdoors, 2) how to capture a wave in a pipe and measure its wavelength, and 3) that the speed of sound depends only on the medium through which it travels.
What you’ll need: Part 1 Stopwatch or stopwatch function on your phone Bell tower that chimes on the hour
Part 2 Deep bucket or sink Piece of plastic pipe or other tube Pencil and ruler Computer with headphones or earbuds and Audacity program, or a tone
generator app on your smartphone Willing assistant
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What you’ll do: Part 1
1) This direct method works if you live in or near a town that has a bell tower that chimes on the hour, perhaps on a city building or a church. If you don’t, come to Kent for a morning or afternoon. Kent has two chimes – the University Library, and St. Patrick’s Church on N. DePeyster Street, just east of downtown. With a stopwatch or other timer that will run for more than an hour, stand as close to the tower as you can, just before any given hour. Decide when in the cycle of chimes to start your timer. Both towers in Kent play the four-line Westminster chime before the actual gongs for the hour, so if I were doing the experiment, I would use the Westminster chime as a ‘get-ready’ signal, and then start timing on the first gong following the chimes. Let the timer run; do not disturb it!
2) Go to a place in town where you can hear the tower from some distance, at least a few blocks, away. For a good guideline, if you can still see the tower or church but in the distance, you are probably in a good spot. Have lunch or talk with a friend for a while. Then, just before the next hour, wait for the same chime sequence and stand ready. At the same point in the cycle as before, stop the timer.
Now, had you been in the same place both times, your timer would read exactly one hour. But it won’t, since you moved a distance away from the tower. The extra time is the time required for the sound of the gong to travel the distance between the tower and your new location. In other words, subtract one hour from the time you measured, and that is the travel time for the sound. Record that time, in seconds, on the Report Sheet.
3) At your convenience go to Mapquest or Google Maps on your computer and generate a map that includes both the tower location and the spot where you stood an hour later. Locate them precisely on the map; it may help to print it out and mark the spots carefully on the printed map. Measure the distance between the two points as accurately as possible using a metric ruler. Then measure the length of the metric distance scale on the map. Set up a simple proportion:
number of meters on distance scale distance from tower -------------------------------------- = ------------------------------ length of distance scale on map distance on map
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A portion of the Google Maps image for Kent State University. The lower red X marks the location of the bell tower, where the chimes are housed. The upper X designates where I was standing while recording the introductory video for Lab 4. Notice the distance scale in the red oval.
Cross-multiply and solve for the distance from the tower. We want the distance in meters, and as you see from inside the red oval on this map, Google Maps measures in feet. But that is no problem for Physics students! Simply divide the number of feet that the sound traveled by 3.28 feet per meter. Record that distance on the Report Sheet.
4) Divide the distance from Step 3 by the time from Step 2, and round off to a whole number. That’s one estimate of the speed of sound.
5) Find and record the outside air temperature in oC. If you can only find the temperature in oF, check Google for how to convert the temperature to oC.
Part 2
6) You know that for any wave, v = f ë. Here you will use a computer program or a phone app to make a sound wave with a known frequency, and a wavelength that you can measure. Multiplying those together gives the speed of the wave.
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Resonance is that easy transfer of wave energy from one object to another when the frequencies match. One object is an earbud or phone producing a sound of known frequency, and the other is a column of air in a small piece of plastic pipe or other tube, where you will adjust the length of the air column until its frequency matches the tuning fork. You’ll know they match because the air in the pipe will ‘sing along’ with the earbud!
If you happen to have some plastic pipe around the house, from 3/4" to 2" diameter and a pipe cutter, lop off a section about 18 inches (or 45 cm) long. Now don’t laugh; some people out there will actually have that lying around. For those of you who do not include pipe cutters among your possessions, you have many inexpensive options. Lowes and Home Depot both sell two-foot long sections of plastic pipe of many different diameters. Lowes also has a great item for this experiment, a 16 inch long straight piece of plastic pipe for sink drain repairs.
Even cheaper, and more available for some of you, is the plastic tube that some golfers use in their golf bags to keep the club shafts from rattling into one another. You can buy a long tube for only a couple of dollars and cut it into 16 in or 18 in long pieces with good scissors or a razor knife. Any sporting goods store will carry those tubes.
You could even use the cardboard tube from a roll of paper towels. It will get soggy, but will last long enough for your purposes.
And in case none of those will work for you, we have included in your free packet for this course a sheet of transparency film that you can roll into a straight tube about an inch or two in diameter, and then tape closed along the edge.
You’ll also need a container of water about as deep as the pipe is long. You may have a bucket around, or a deep washtub sink. The five gallon paint buckets that both Lowes and Home Depot sell for only a few dollars are great – and useful for lots of other stuff after the course is done.
Do you have a tall vase? That would be perfect. Or an aquarium? Or a bathtub? Depending on its design, you could even use a toilet – everybody has one of them. Be sure to flush first!
The more shallow the container, the higher the frequencies you will have to use, because you already know that the higher the frequency,
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the shorter the wave. Remember, it’s not the width or volume of the container that matters, only the depth.
7) Fill the container or sink so that the water is almost as deep as whatever pipe or tube you are using. If you use the transparency sheet in the packet, hold it gently so that it stays round, and keep the zero end of the scale printed on it toward the top.
8) Plug headphones or earbuds into the audio output of your computer. Run the Audacity program that you used previously, but now you will use it to generate a tone. Click Generate, then Track. In the pop-up, choose Sine and an amplitude of 1. Enter a frequency in the approximate range of 180 Hz to 500 Hz, then click OK. Record the frequency in the data table on the Report Sheet for this lab.
If you have a smart phone, you could also download any free app that generates musical tones. For my Android phone, I found one called – guess what? – Tone Generator. In that case you would hold the speaker of the phone above the tube, in place of the computer headphone, as pictured.
9) Click the Play button (|) in Audacity, or have a friend click it. With one hand, hold the pipe straight up so that the lower end is just under the water. With the other, hold the headphone or earbud at the upper end of the pipe. If you are using a headphone, leave a little space between it and the upper end of the pipe, as shown.
Then smoothly and gradually slide the plastic tube and headphone downward, together as one unit, until you suddenly hear a louder sound. It’s louder because the air in the pipe is now in resonance with the headphone! You could say that the air inside the tube is singing along with the headphone, so the sound is louder. Move the pipe up and down just a little to find the loudest resonance. While you hold very still, your assistant can use a pencil to mark the water level on the plastic tube, as accurately as possible. Then you can stop the annoying sound source.
10) If you are using the tube you rolled up from your packet, you or your assistant can measure the level of the water right on the printed scale. If you are using any other kind of tube, remove it from the water and measure and record the length of the air column in the tube, which is the distance from the top of the tube down to the pencil mark. It’s better to measure in centimeters, but if you must use inches, multiply the
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Since the pens lie diagonally, a pen a little longer than the cup still fits inside it. In the same way, we have to allow for the diameter of the pipe that ‘holds’ the wave.
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length by 2.54 cm/in, and record it in the second column in the table, L in cm.
11) Divide the length of the air column that you measured by 100, to change the units to meters, and record that number in the third column.
In a pipe closed at the bottom, only one-fourth of the wave is caught in the pipe in the fundamental mode. So, you should be able to multiply the length of the air column by four to find the wavelength.
Now I wrote ‘should’ because in fact a pipe such as this one holds exactly one-fourth of a wave only if the pipe is very narrow compared with the wavelength. (If we used such a pipe – a glass tube from chemistry, or a really long straw – the sound in the tube is too faint to hear.) Acoustic books tell us that the proper formula, including the effect of the diameter of the pipe, looks like this:
ë = 4 (L + 0.30 d)
where L is the length of the air column in meters and d is the inside diameter of the pipe, also in meters.
Measure the inside diameter of the pipe you used, ideally in cm. If you used inches, multiply by 2.54 cm/in. Then divide that number by 100 mm/m and multiply by 0.30. As an example, suppose you used the plastic pipe for drain repair from Lowes. It is sold as 1-1/2" outside diameter, but inside, I measure it as 1-3/8.” That is 1.375 inches times 2.54 cm/in, or 3.49 cm. Dividing by 100 yields 0.0349 m, and multiplying that by 0.3 gives 0.0105 m (or 0.011 m). The equation now becomes
ë = 4 (L + 0.0105)
where L is in meters. Evaluate the expression and enter the wavelength in meters in the fourth column of the table on the Report Sheet.
12) Since v = f ë, multiply the frequency (the first column) times the wavelength (the fourth column) to find the speed. Round it to the nearest whole number and enter it in the fifth column.
13) Repeat steps 8 through 12 with four other frequencies. Since the speed of sound depends on the medium, the numbers in the last column should be about the same. Average them out and again round to the
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nearest whole number. Record that number, your result from Part 1, in the last box in the table on the Report Sheet.
14) Almost done! Find a good estimate of the indoor temperature where you did your experiments, in oC. If you can only find the temperature in oF, check Google for how to convert the temperature to oC. Sound propagates at 331 m/s at zero oC, plus 0.6 m/s for each degree. For example, at 20 oC, sound waves advance at 331 m/s plus 20 times 0.6 m/s, or 331 m/s plus 12 m/s, or 343 m/s. See how that works?
Record the expected speed of sound for both Parts 1 and 2 on the Report Sheet as well.
15) Finally, evaluate your results. How well did each method measure the speed of sound? That is, which method produced a result closer to the expected speed of sound? Speculate on why that method might have been more reliable.
Web extension
Browsing the web, I found sites claiming that at least three different people first measured the speed of sound in air. Carry on the search – find the earliest date that someone actually measured the speed of sound. Tell me who did it, how, and when.
Be sure to include the basic web address where you found your answer.
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