SPEED OF SOUND
Sound waves passing through the air cause air molecules to move back and forth parallel to the
direction that the wave is traveling. This back and forth motion of the air molecules results in
alternating regions of high pressure and low pressure. A region of high pressure is called a
"compression," and a region of low pressure is called a "rarefaction." The time it takes for a
region to be compressed, and then rarefied, is called the period (T). It is measured in seconds.
The number of times that a region is compressed in one second is called the frequency (f).
Frequency is measured in Hertz (Hz), which is the inverse of a second. The wavelength (λ) is the
physical distance from one point of compression to the next, and it is measured in meters. Using
a microphone, we can determine the frequency of a sound by graphing air pressure versus time
and observing the pattern set up by the constantly changing volume. This pattern is called a
waveform.
Figure 1.
A disturbance, such as a finger-snap, will cause the movement of air molecules as described
above. These air molecules disturb adjacent molecules, creating a domino effect that causes the
wave to propagate outward. The velocity of the wave, known as the speed of sound (Vs),
describes the distance that a sound wave travels outward in a certain amount of time, or the
wavelength (λ) divided by the period (T). It has units of m/s.
v = d/t; v = λ/T
(Eq. 1)
This speed is related to density and stiffness of the material that it is moving through. The speed
of sound is also temperature dependent:
v = 331 m/s + T(0.6 m/soC)
(Eq. 2)
where T in the above equation is the temperature (not the period) in degrees Celsius.
Consider a continuously produced tone, like the sound generated by a tuning fork. If there is a
hard surface to reflect the sound, the echo will double back and interfere with the tone that is
coming from the fork. The sound heard is then the sum of the tone and its echo. If the tone
doubles back on itself in a way that is symmetrical, with the compressions due to the echoes in
the exact same positions as the compressions due to the original tone, then the pressure will be
doubled. This will result in a noticeable change in volume. In order for the sound to interfere in
this way, the reflective surface has to occur at the exact center of a compression or a rarefaction.
This constructive interference is called a standing wave.
MATERIALS
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Variable-length resonance tube
Computer and LabPro
Various tuning forks
Thermometer (at the front desk)
CAUTION: DO NOT STRIKE THE FORKS TOGETHER OR ON A HARD SURFACE!!!
ACTIVITIES
Activity 1: Calculating the speed of sound based on room temperature
Record the temperature inside the variable-length resonance tube. Calculate the speed of sound
in the lab based on the current temperature.
Activity 2: Using frequency and wavelength to determine the speed of sound.
Since the period of a wave is the time it takes to travel the distance of one wavelength, the period
and wavelength may be used in the v = d/t equation to determine the wave velocity (see Eq.1).
According to Eq. 2, the speed of sound in air only varies with temperature. If this is true, then v
will be constant for all values of λ and T. Therefore Eq. 1 may be restated as a linear equation in
the form y = mx:
λ = vT
where v is a constant and is the slope of a λ vs. T graph.
The wavelength (λ) can be found by measuring the distance between the centers of compression
and rarefaction. As you can see in Figure 1, the distance from the center of a compression to the
center of a rarefaction is exactly one half of the wavelength. In this experiment, you will hold a
tuning fork at the entrance of the tube. As you vary the tube length, listen carefully for a sudden
increase in volume. High volume indicates that a standing wave has been created and the
vibrations are interacting constructively. That only happens when the end of the tube is located at
the exact center of a compression or the exact center of a rarefaction. Therefore, the distance
between two compression points is equal to one half of the wavelength. Use this idea to
determine the wavelength of the tones produced by five different tuning forks.
Stamped on each fork is its frequency. Using this given information, calculate the period of the
tone produced by each fork.
Create a linear graph that will allow you to determine the speed of sound. Compare this value to
the value found in Activitity 1 using percent difference. Print this graph.
POSTLAB QUESTIONS
1. For a wave that is travelling at a constant velocity, what is the relationship between
frequency and wavelength? Explain in words.
2. Summarize Activity 3 in your own words.
3. Carefully examine the temperature-dependent speed of sound equation used in activity
one. Can this equation be modeled with a linear equation? If so, what are the independent
and dependent variables? What is the significance of the y-intercept? What is the slope,
and what are the units of the slope? Sketch a graphical representation of the temperature
dependence of the speed of sound from -10 oC to 30 oC.