Experiment VWS-4S
1
VELOCITY OF SOUND IN AIR
Purpose
The purpose of this experiment is to measure the velocity of sound in air by the resonance -tube method.
Community College of Philadelphia
Physics Department
Student Name:
_____________________________________________________
Partners:
_____________________________________________________
_____________________________________________________
_____________________________________________________
Physics Course #:
____________________
Section #:
___________________
Date performed:
____________________
Date due:
___________________
Experiment VWS-4S
2
VELOCITY OF SOUND IN AIR
Purpose
The purpose of this experiment is to measure the velocity of sound in air by the resonance -tube
method.
Theory
Wave motion is hardly an unusual phenomenon. Sound waves, light waves, and radio waves, to name
just a few, have considerable effects upon our daily lives. Although at first glance the many types of
waves which we experience may seem to have very little in common, further study reveals that in certain
respects one sort of wave motion is much like any other.
Any type of wave motion is capable of transmitting energy from one location to another by creating a
disturbance which propagates through a medium. Interestingly, the medium need not always be a
physical medium. Light waves, for instance, will propagate through a vacuum. If a physical medium is
involved, however, individual particles of the medium will oscillate up and down or back a nd forth but
will not progress with the wave. Although energy is transferred, the particles themselves remain close to
their original positions.
Waves are conveniently classified by the way in which the motion of the individual particles of the
medium is related to the movement of the wave itself. A wave in which the vibrating particles move at
right angles to the direction in which the wave travels is known as a transverse wave. A wave in which
the individual particles vibrate along the direction of p ropagation is known as a longitudinal wave.
Consider the sound wave generated in air by the tuning fork of Figure 1. The vibrating prongs of the
fork strike nearby air molecules and set them in vibration. These air molecules collide with other air
molecules farther from the tuning fork and cause them to vibrate also. Soon, groups of air molecules
within a considerable distance of the tuning fork are vibrating back and forth with the same frequency as
the vibrating prongs of the tuning fork. (The vibra tions of the air molecules are, of course, superimposed
on the normal random thermal motion of the molecules.) As a result of the molecular vibration, there are
certain regions where the air molecules are closer together than normal and where the pressure is slightly
higher than the normal atmospheric pressure. These regions are known as regions of compression and are
marked with C's in Figure 1. There are other regions where the air molecules are farther apart than
normal and where the air pressure is slightly less than the normal atmospheric pressure.
Figure 1
Traveling Sound Waves Generated by a Tuning Fork
C
Tuning
Fork
C
Ear
C
v
R
R
R

Experiment VWS-4S
3
These regions are known as regions of rarefaction and are marked
by R's in Figure 1. As the tuning fork vibrates, these reg ions of
compression and rarefaction move outward from the fork in
various directions, including that toward the ear of the listener.
As the compressions and rarefactions pass the ear, the eardrum
vibrates and the listener hears the sound of the tuning for k. Since
the air molecules vibrate in the same direction as the wave is
moving, a sound wave in air is an example of a longitudinal
wave.
The velocity of propagation of the compressions (and
rarefactions) in Figure 1 is the speed of sound v. The speed of
sound in air is approximately v 0 = 331.3 m/s at 0 o C. At higher
temperatures the speed of sound v t is somewhat higher and is
Figure 2
Resonance-Tube Apparatus
Plastic
Tube
Air
Centimeter
Scale
Water
Reservoir
given by equation (1), in which t c is the temperature in o C.
vt  vo
273.2  t c
(1)
273.2
The number of compressions per second passing a point in
space (such as the ear) is known as the frequency f of the wave.
This frequency is the same as the frequency of vibration of the
source, providing that there is no relative motion between the
source and the ear of the listener. The units of frequency are
given the name hertz (abbreviated Hz). The distance from the
middle of one compression to the middle of the next is called the
wavelength. The wavelength is represented by the Greek letter
lambda () and may be expressed in units of meters. The
velocity, frequency, and wavelength are related by equation (2).
v
=
f 



(2)
In this experiment we will assume f to be the frequency of the
tuning fork as specified by its manufacturer; we will measure 
by the resonance-tube method; and we will determine our
measured value of v by substituting these quantities in equation (2).
Water
Rubber
Hose
Support
Rod
Figure 2 is a diagram of the resonance-tube apparatus to be used in this experiment. A hollow plastic
tube, a centimeter scale, and a water reservoir are supported from a vertical rod. The lower end of the
plastic tube is connected to the water reservoir by a piece of rubber hose. The water level in the plastic
tube can be varied by raising or lowering the water reservoir. In this way changes can be made in the
length of the air column in the plastic tube above the water. It is possible that you may be given a
slightly different apparatus on which the centimeter marks are placed directly on the plastic tube i nstead
of on a separate meter stick. There may also be a difference in the clamp that holds the water reservoir on
the rod.
Suppose that a vibrating tuning fork is held above the tube as in Figure 3. A sound wave travels
down through the air column in the top of the tube and is reflected back upward from the water. The
wave is partially reflected again at the open top end of the tube. These waves traveling upward and
downward in the tube combine to form a "standing wave". In the standing wave there a re certain fixed
regions called nodes where there is very little vibration of the air molecules. In the standing wave there
are other fixed regions called antinodes where there is a large vibration of the air molecules. Each
antinode is separated from the nearest node by a distance of /4, where  is the wavelength of the original
traveling wave.
Experiment VWS-4S
4
There are certain lengths of the air column (in relation to ) for which the vibrations of the air
molecules at the antinodes are especially large. This condition of the air columns is k nown as resonance.
At resonance the energy is removed more rapidly from the tuning fork and the sound becomes louder.
Figures 3 a, b, and c show the three resonance conditions possible with your apparatus. The nodes of
displacement are marked as "N" and the antinodes are marked as "A". Note that in each resonant case
there is a node at the bottom of the air column and an antinode at the open end of the tube. Your
apparatus can be adjusted for the three resonant conditions by listening for increases in t he loudness of
the sound of the tuning fork. The wavelength can be calculated from the length of the air column at
resonance. Finally, the speed of sound in air can be calculated using equation (2).
Figure 3
Resonance in the Air Column
a
A
N
l = 
4
b
c
A
A
N
l =
A
N
3
4
N
A
N
A
N
Apparatus
Resonance-tube apparatus
Tuning fork (512 Hz)
Tuning-fork activator
Beaker (1000 ml)
Stethoscope
Centimeter scale
5
l =
4
Experiment VWS-4S
5
Procedure, Data, and Calculations
Cautionary Notes:
a. Water is sometimes spilled accidentally during this experiment. It is
advisable to keep books and other personal property of the table where you
are using the resonance-tube apparatus.
b. A stethoscope is provided if you have difficulty hearing the sound from your
own resonance tube. Its earpieces have been sterilized with alcohol. No
more than one lab partner should use the stethoscope because of the danger
of spreading an ear infection.
1.
Measure and record the room temperature to the nearest tenth of a degree Celsius. Read the
frequency engraved on the tuning fork and record it on the data table. Measure the inside diameter of
the plastic resonance tube with a centimeter scale and record these values below and on the data table.
Room temperature:
t r = ____________________ C
Frequency of tuning fork:
f = ____________________ Hz
Inside diameter of tube:
D = ____________________ cm
2.
Set the reservoir cup of the apparatus as high as it will go on the metal rod (i.e., until it bumps into
the bracket supporting the top of the plastic tube). Be sure that the rubber tubing is tightly attached at
one end to the reservoir and at the other end to the bottom of the plastic tube. Verify that the water
level is approximately 14 cm below the top of the tube. If the level is too low, pour water from a
beaker into the reservoir to correct this.
3.
Strike the tuning fork on the rubber activator. Hold the tuning fork over the plastic tube with one
prong directly over the other prong.
4.
Slowly lower the water level in the plastic tube by lowering the water reservoir. Adjust the water
level until the sound of the tuning fork is reinforced by resonance in the column of air above the
water. It may be necessary to reactivate the tuning fork several times while searching for the water
level at which the sound of the tuning fork is loudest. You will need to read the water level while it
is changing at the instant the sound is loudest. Read the scale next to the plastic tube at this water
level to the nearest .02 cm. Record this reading as the resonant length l .
Length of resonant column
of air (reading 1):
5.
l = ____________________ cm
Correct this value of the length of the air column by adding four -tenths of the diameter of the plastic
tube. This correction is necessary because the antinode is not formed at the tube opening, but a little
outside of it.
l corr = l + .4 D
=
= ___________________ cm
(Substitute)
(Final answer)
Experiment VWS-4S
6
6.
Since the first resonance occurs at l corr = /4, the wavelength can be calculated by rearranging this
formula.
 = 4 l corr =
(Substitute)
= ___________________ cm
(Final answer)
7.
Transfer the measured and calculated data from steps 4, 5, and 6 to the data table for reading 1.
8.
Strike the tuning fork on the activator again and hold it above the resonance tube. Lower the water
level until a second resonant condition is reached. Record this level on the data table as l for
reading 2. Lower the water level further until a third resonant condition is reached. Record this level
on the data table as l for reading 3.
9.
Correct these two additional values of l in the same way you did in step 5. Then calculate the
wavelengths. For reading 2:  = 4 l corr /3. For reading 3:  = 4 l corr /5. Make these calculations
on scratch paper and record you results on the data table.
10. Calculate the average wavelength below. Then, convert this wavelength to meters by moving the
decimal point two places to the left.
average  =
Sum of 3 values
3
=
(Substitute)
= _______________ cm = _______________ m
(Final answer)
11. Calculate the velocity of sound from your measurements. Use t he average value of  from step 10.
v meas = f  =
(Substitute)
= ___________________ m/s
(Final answer)
12. Find the accepted speed of sound at your room temperature.
v accept  331 .3
273 .2  t r
273 .2
=
(Substitute)
= __________________ m/s
(Final answer)
13. Calculate the percent error in your measured value of the speed of sound.
% Error =
v meas  v accept
v accept
 100
=
= ___________________ %
14. Transfer the results of your calculations in steps 10 through 13 to the data table.
(Substitute)
(Final answer)
Experiment VWS-4S
Data Sheet
Experiment VWS-4
7
Room temperature:
tr
= ____________________ o C
Tuning-fork frequency:
f
= ____________________ Hz
Inside diameter of plastic tube:
D
= ____________________ cm
Determination of wavelength 
Item
Reading 1
Reading 2
A
A

A
N
Reading 3
l =
4
N
Diagrams showing
l=
A
nodes and
3
4
N
N
A
N
antinodes of
l =
5 
4
A
displacement
N
 = 4 l corr
l
(Step 4)
l corr = l + .4 D
(Step 5)
cm
 = 4 l corr /5
cm
cm
cm
cm
(Step 8)
cm
(Step 6)

 = 4 l corr /3
cm
(Step 9)
cm
(Step 9)
cm
Average = ____________________ cm = ___________________ m
v = f
Measured velocity at room temperature:
Accepted velocity at 0 o C:
Accepted velocity at room temperature:
vo
vt  vo
Percent error in measured velocity of sound:
= ___________________ m/s (Step 10)
= ___________________ m/s (Step 11)
273.2  t r
273.2
= ___________________ m/s
(Step 12)
___________________ %
(Step 13)
8
Experiment VWS-4S
Questions
1.
Was your value of the velocity of sound approximately equal to the accepted value, within a
reasonably small percent error? What specific defects in the equipment or procedure might have
contributed to your error?
2.
If the temperature of the room had been lower, would the length of the resonating air column been
affected? Explain.
3.
Why do you see a flash of lightning before you hear the corresponding clap of thunder (instead of at
the same time)?
4.
Mention some musical instruments that use hollow tubes or hollow cavities to obtain a resonant
condition of the air in the tube or cavity.