The Sonometer and Strings
THE SONOMETER AND STRINGS
By Joe Laszlo, Ph.D.
Background: The sonometer is a device that enables you to determine the relationship between the tension or force pulling on a vibrating string and the frequency it produces and the length of a vibrating string and the frequency it produces.
Materials: a sonometer consists of a board with two monofilament strings each being one meter long between the inner bridgepiece and the end bridgepiece. String A. is attached to an anchor on the board near the inner bridgepiece and has a loop on the other end, hanging over the end bridgepiece. Masses attached to the loop cause tension on it. String B is attached to the board below the end bridge piece, with the other end attached to a tuning peg. Turning the tuning peg enables the string to be tuned to a given frequency (Figure 1). Also included is a set of tuning forks, a tuning fork mallet, a fret piece, a meter stick, and masking tape.
Part 1 Tension and Frequency.
Problem: What happens to the frequency of a vibrating string as the tension or the force on the string is increased?
The frequency of a string is how high or how low the sound is when the string is plucked.
1. Clamp the sonometer onto a table top with a “C” clamp near the tuning peg end and with the end bridgepiece over the edge of the tabletop.
2. Hang a kilogram mass on the end of String A. Pluck the string. Listen to the frequency of the string. Is it high or low? Make a data table with a column for tension and one for frequency. Describe the change in tension and the change in frequency qualitatively, as you add weights to the free end of the String A.
3. Add another weight to the free end of String A (Figure 2). Pluck the string. How does the frequency of the string compare with the pitch you heard for the first trial? Enter your data into the table.
3. Do two additional trials by adding additional weights to the free end of String A, plucking it and determining the change of frequency of the string. Record your results into the data table.
Summary Question
1. What is the relationship between the change of tension caused by the addition of weights on the vibrating string and the frequency of the String A? Is this what you would logically expect to happen as the tension changes? Explain your answer.
Part 2. Length of the String and Frequency
Background: In this part of the sonometer activity you will be using a number of tuning forks. To cause a tuning fork to vibrate, strike it with the rubber mallet provided at the midpoint of one of the tines. NEVER STRIKE A TUNING FORK ON A HARD SURFACE. TO DO SO WILL CAUSE IT TO BECOME WARPED AND USELESS.
Problem: What is the change in frequency of a vibrating string as the length of the string is changed?
1. Put a piece of masking tape on the sonometer board under String B the entire length of the string from the inner bridgepiece to the end bridgepiece. As you change the length of the string, you may make pencil marks on the tape, BUT NOT ON THE BOARD (Figure 3). Remember that the open string is 1 meter long.
2. Strike the tuning fork that is the musical note C at 256 Hz, and put the handle of the tuning fork against the sonometer board. This will cause the sonometer board to resonate. Tune String B to 256 Hz by changing the tension by turning the tuning peg to which the string is attached.
3. Make a data table with two columns: one for length of string and the other for the frequency of the string when plucked. The frequency can be found stamped into the tuning fork you used to identify the frequency of the vibrating string. Your first entry will be frequency 256 Hz with a length of 1 meter.
4. Find the tuning fork with the next highest frequency above 256 Hz. Strike it and place the handle onto the sonometer board. Using the fretpiece, shorten the string starting from the inner bridgepiece end while plucking the string until you find the length that is in tune with this tuning fork. Mark this place on the masking tape. Measure the length of the vibrating portion of the string and enter it into the data table along with the frequency stamped onto he tuning fork.
5. Repeat step 4 above with each of the remaining tuning forks. Record readings into the data table.
6. Measure the room air temperature and enter it into your data table.
7. When complete, one partner will enter your group’s data into the class data table on the chalkboard.
8. Make a copy of the class data for yourself.
Graphing: You will plot two graphs. One will be of your group’s data, the other of the class data. Make a graph of the frequency and length of the plucked string data. Use the length as the independent variable on the X-axis and the frequency on the Y-axis.
Summary Questions
1. What is the shape of the curve on the graph of your group’s data?
What is the shape of the curve on the graph of the class data?
Explain why the curve is the shape that you described above.
2. Give reasons why you were asked to make a graph of the class data.
3. What is the relationship between the change of length of the vibrating string and the frequency of the string? Is this what you would logically expect to happen as the length changes? Explain your answer.
4. Pipes are also used to produce sounds. An example of a pipe that can produce sounds is a trombone. Based upon the above experimentation with vibrating strings, what might happen to the frequency of a sound being produced by a trombone when only the length of the pipe of the slide changes? Explain your answer and your logic.
Extensional Exercise
From this activity you should have gained an understanding of the effect of either a change in tension or a change in the length of the string has on the frequency that it produces. A third factor that can change the frequency of a string is a change in the density of the material of which the string is made.
1. What do you predict that a change in the density of the string would have on the frequency of a vibrating string?
2. How might you do an experiment to prove your prediction? Outline a procedure below. Then do your activity to show the relationship between density and frequency.
Vocabulary
Frequency
Hertz (Hz
Wavelength
Force
Tension
Vibration
Sonometer
Tuning Fork
String
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