Experiment 13 Speed of Sound in Air

Advanced
Reading
(Serway) Chapter 18-3, 18-4 and 18-5
Equipment
Experiment 13
Speed of Sound in Air
open end
• Sound Tube (Fig. 13-1)
• 3 different frequency tuning forks
• mallet to strike tuning fork
• water jug
• rubber hose
• rubber bands
Objective
L
λ/2
The objective of this experiment is to
measure the speed of sound in air in a
tube open at one end and closed at the
other.
Theory
When a sound source of some frequency
is placed at the mouth of an
open-ended tube, the sound will
travel down the tube, be reflected,
and return to the other end of the
tube (Fig. 13-1). For certain frequencies,
the source will reinforce
the sound, and a resonant standing
wave will occur. This allows the ear
to distinctly hear the sound radiating
from the tube.
For an open-closed tube, resonance
occurs when an odd-integral number
of quarter-wavelengths fits in the
tube (Fig. 13-3). In order to achieve
the proper conditions for a given
tuning fork, which means a fixed
frequency and wavelength, one must
be able to change the length L of the
tube. In this experiment, this will be
accomplished by changing the level
of the water in the tube. The difference
in water height corresponding
to successive resonances will be λ /2,
so if one knows the frequency of the
tuning fork, the speed of sound can
be calculated using the relationship
v =λf , where v is the speed, λ is the
wavelength, and f is the frequency.
water
closed end
Fig. 13-3 Resonant condition of an
open-closed tube of length l; a
standing wave occurs in the tube.
Procedure
1. Lift the plastic jug of water to a
height so that the sound tube fills
completely with water. Be careful
not to let the tube overflow.
2. Strike a tuning fork with the
rubber mallet and hold it near the
end of the plastic tube. Be sure to
hold the tuning fork as shown in Fig.
13-2. Place the plastic jug on the
floor and listen for resonances as the
water level falls. Slide the rubber
band that is around the tube so that it
is near the position of the water
when each resonance are heard.
3. Raise the water jug so that the
water returns to the first resonance
position. Fine tune the position by
raising and lowering the water until
the loudest resonance is heard.
Adjust the rubber band if necessary.
Repeat this process for the other resonance
position.

4. The distance between the two
resonance positions should be λ /2.
Use the frequency printed on the
tuning fork and the experimental
value for the wavelength to find the
speed of sound, which is v =λf .
5. Repeat the above procedure for
the other two tuning forks. Calculate
an average value for the speed of
sound.
6. Calculate the theoretical value
for the speed of sound using the
equation v = (331.5 + 0.61T)m/s, where
T is the temperature in degrees
Celsius. Use the thermometer at the
front of the room to measure the
temperature. Calculate the percent
difference between your average
value of the speed of sound and the
theoretical value.
7. There is a table on the board; write your
experimental and theoretical values in the
appropriate places. Determine the class
average for experimental speed of sound, v E
and theoretical speed of sound, v T
.
Questions/Conclusions
1. Why should the tuning fork be
held in the orientation shown in Fig.
13-2?
2. With the values of the speed of
sound determined by all groups, calculate
the mean v, the standard deviation
σ v
, and the standard deviation
of the mean σ v
. The final experimental
value for the speed of sound
is v ±σ v
. Does the theoretical value
lie within this interval?
3. If the theoretical value lies outside
the experimental in question 2,
what could be responsible for this
systematic deviation?

Figure 13-1 Figure 13-2
Apparatus for measuring the
Proper tuning fork orientation.
speed of sound in air.