Experimental Determination of the Dimensions and Rate of Travel of Sound Waves
Laboratory No. 1
Aims:
How can we experimentally determine the length of a sound wave?
How can we determine the rate of travel of sound waves in air?
How does air temperature affect the propagation rate of sound waves?
How can we better understand wave frequency and its calculation?
How are the wavelength, frequency, and speed of sound waves interrelated?
Objective: Through the use of a resonance tube, a glass cylinder, and a tuning fork of known frequency, students will be able to measure the wavelength and speed of sound waves in air
Introduction. A sound wave travels too fast to be timed directly with simple laboratory devices. The speed v of a sound wave may be measured indirectly, however, by first determining its wavelength from a sound source of known frequency. Then v may be found from the relationship v = fl where f is the known frequency of the vibrating (source) body and l is the wavelength of the sound wave. A tuning fork is a device that is designed to vibrate at a known and constant frequency which produces sound waves of the same frequency. The frequency of all laboratory tuning forks is stamped directly on the body of the fork, just above the connection between the handle and the tines. The wavelength of the sound waves produced by a vibrating tuning fork may be determined by holding the fork over the air column formed by a glass tube that is slipped into a larger diameter resonance tube partially filled with water while sliding the glass tube up and down. As such, the length of the air column is varied until a significant increase in volume (loudness) of the sound emerging from the tube is heard. When this occurs, the air column is said to be in resonance with the tuning fork. This means that the air column has been set into vibration at its natural frequency. The vibration amplitude at resonance is so great that the loudness of the sound is multiplied many times. For a given tuning fork, especially one of high frequency, you may be able to find several resonant lengths. In this experiment, however, you will be primarily interested in measuring the shortest air column that will produce resonance.
For the shortest resonance column, it ca be shown that the length of the air column is l/4. It is this relationship that will enable you to obtain the information you need to determine the speed of the sound wave in the air column. Throughout this experiment, you must be sure that the lower end of the glass tube is submerged beneath the surface of the water (see diagram below) so that you will be working with a tube that is closed at one end.
d
L'
Lab Stand
Lab Table
Water Level
(Resonant Surface)
Clamp
Graduated
Cylinder
Water
[Resonance Tube]
Glass Tube
Setup. Arrange the equipment as illustrated in the diagram above. The tall (1000 ml) graduated cylinder (resonance tube) should be nearly full of water and the glass tube should be able to easily slide within it. Addition of a few drops of food coloring to the water column will make for easier observation of the resonant (water) surface.
Strike a selected tuning fork on the green rubber striker to initiate vibration of its tines. Hold the vibrating fork at the level of the mouth of the glass tube with its tines vibrating toward and away from the water surface. Then slowly raise both the glass tube and the vibrating tuning fork, keeping the relative position of the tube and fork constant while listening for maximum tone.
You may have to practice a number of times until you find the shortest air column length L' that produces resonance. The effect at resonance is unmistakable: the increase in tone loudness is very noticeable. To set the air column at exactly the right resonant length, move the glass tube up and down alternately, gradually reducing the motion until you have pinpointed the resonance position. To help you distinguish your particular sound from the multitude of other sounds coming from your classmates' equipment, remove the tuning fork, and then quickly replace it over the resonant air column.
Experiment has shown that the length of the resonant air column determined as just described requires a small correction because of a phenomenon called end effect. This phenomenon causes the air column at resonance to be slightly longer than the measured air column length (L'). The corrected length of the column is is obtained by adding 4/10ths of the inside diameter of the glass tube (d) to the measured length of the air column (L'). Corrected resonant length (L) is found as follows:
L = L' + 0.4d
where L is corrected air column (resonant) length (in cm), L' is measured air column (resonant) length (in cm) and d is inside tube diameter (in cm).
Equipment.
q Glass Cylinder (~46 cm minimum length)
q Resonance Tube (~56 cm minimum length) or 1000 ml graduated cylinder
q 256 Hz Tuning Fork
q 512 Hz Tuning Fork
q Tuning Fork Striker (green rubber)
q Meter Stick
q Celsius Thermometer
Procedure.
(Note: All measurements are to be taken in cm, recorded to the nearest 0.1 cm.)
1. Note and record the frequencies of both tuning forks.
2. Using the green rubber strikers, set one tuning fork into vibration and find the shortest air column length that will produce intensified sound as outlined previously. Measure distance L', which is the distance from the water surface to the top of the glass tube and record. Repeat two additional times and record. Average all three trials and record. Measure room air temperature in degrees Celsius and record.
3. Repeat Step 2 above for the second tuning fork.
4. Measure and record the inside diameter (d) of the glass tube.
Data.
Frequency of Tuning Fork 1 __________HzFrequency of Tuning Fork 2 __________Hz
v = 331 + 0.6(T) where T is room air temperature in degrees Celsius, without units.
The unit of speed in this expression is m/s.
v = __________m/s
Questions.
1. a. Calculate the Percent Error between your Experimental and Actual speeds of sound.
b. On the basis of your calculated PE values above, is the resonant tube method a
reasonable one for determining the speed of sound? Explain.
2. Does the speed of sound vary with changes in its frequency at constant temperature?
Explain.
3. To obtain the actual speed of a sound wave, modify the equation v = fl so as to
permit you to substitute directly the values for frequency, uncorrected tube length of
resonating column, and the end effect correction. Show all work.
4. State the relationship between frequency and corrected length of the resonant air
column.
5. What effect does a decrease in air temperature have on the
a. frequency of the wave.
b. wavelength,
c. speed of the wave, and
d. length of the resonant column?
Assembled
Apparatus
Air Column
Strategy. For a tuning fork of known frequency (f), you will determine the length of a resonant air column (L') by listening for greatly intensified sound. After making a mathematical correction for the length of the air column, you will determine the wavelength of the sound wave from the length of the air column and then calculate the speed of the sound wave from the relationship v = fl. You will repeat these measurements with a tuning fork of different frequency and thus obtain a second value for the speed of sound wave. After determining the accepted value of the speed of a sound wave at the temperature of your equipment, you will then be able to compare your measured (experimental) values with the accepted (true) value.
For the shortest resonance column, it ca be shown that the length of the air column is l/4. It is this relationship that will enable you to obtain the information you need to determine the speed of the sound wave in the air column. Throughout this experiment, you must be sure that the lower end of the glass tube is submerged beneath the surface of the water (see diagram below) so that you will be working with a tube that is closed at one end.
