PHY124
Lab # 2 Speed of Sound
Introduction
Sound is a longitudinal (mechanical) wave that travels through an elastic medium.
When the sound wave is traveling through air, the (approximate) speed of sound can be
calculated from the air temperature as follows:
m
m
Speed of sound  331  0.6 s TC 
s
C
The speed of sound will vary with other factors as well (air pressure, humidity,
particulates in suspension) but the main factor that causes the speed of sound in air to
change near the surface of the earth is air temperature. The speed of sound when the air
temperature is 0 degrees Celsius is 331 meters per second. This speed increases by about
0.6 meters per second for every 1 degree Celsius increase in temperature. When a sound
source is placed above a hollow PVC pipe, some of the sound waves generated will travel
down the length of the pipe. When the bottom of the tube is reached, the sound waves
will be inverted as it gets reflected and travels back up through the air in the PVC pipe. If
the length of the PVC pipe is equal to about ¼ of the length of a wavelength of the sound
wave, then the reflected wave as it leaves the pipe will be in phase with next sound wave
passing down into the tube. This causes a standing wave to be set up inside the PVC pipe
with a node at the closed end and an antinode just above the open end. The node (a point
of no displacement) forms at the closed end because the air at this point has no place to
move. The air at the open end of the tube vibrates back and forth in and out of the PVC
pipe with the maximum displacement, so you get an antinode near the top of the pipe.
Although your textbook says that the antinode will form at the open end of the pipe, the
antinode actually forms at a point just above the open end of the tube. (This distance is
needed to equalize the air pressure of the antinode position with atmospheric pressure.)
The distance above the end of the PVC pipe that must be added to the length of the pipe
is called the "end correction factor" and is equal to about 0.4 times the inside diameter of
the PVC pipe. Therefore the length of the soundwave formed when the air inside the pipe
resonates can be found as follows:
Wavelength = 4(L + 0.4D)
Where: L = length of PVC pipe above water
D = inside diameter of PVC pipe
Remember also: wave speed = (frequency)(wavelength)
v  fλ
The sound source used in this lab will be a tuning fork. The tuning forks will have both
a letter and a number stamped on them. The letter is the musical note. The number is the
frequency in Hertz that the tines (or legs) of the tuning fork will vibrate at when it is
struck. Note: it is important to not strike the tuning fork on anything hard. The frequency
that the tuning fork will vibrate at is determined by the material that it is made out of and
the physical dimensions of the tuning fork. If the tuning fork is bent, scratched or dented
it will change the frequency that it will vibrate at. Note: you should stop the tuning fork
from vibrating before you put it down on the table.
When the tuning fork is struck the air around the tuning fork will be forced to vibrate at
the same frequency that the tines of the tuning fork are vibrating at. The faster the tines of
the tuning fork vibrate, the higher the frequency of the vibrations of the air around the
tuning fork. All of the marked tuning forks in the lab are made out of the same materials
and have the same basic dimensions. What makes the tuning forks vibrate at different
frequencies is the fact that the tines of the tuning forks have different lengths. The longer
the tines of the tuning fork (all other things being equal) the longer it will take for them to
vibrate back and forth. This means that the period of the sound waves created by the
tuning forks increases with an increase in the length of the tines. Therefore the longer the
tines (legs) of the tuning fork, the lower the frequency of sound produced when it is
struck. Note: the speed of sound does not change unless the air temperature changes.
Therefore as the frequency of the sound source increases, the wavelength decreases.
In a situation where there are two sound waves with the same frequency traveling in
opposite directions through the same material (provided the sources of these sound waves
are stationary) there will be certain locations where the two waves always interfere
constructively and other locations where they always interfere destructively. The pattern
that forms is called a “standing wave”. The locations where the waves always interfere
destructively are called nodes. (A node is a point of no displacement of the medium in a
standing wave.) The locations where the waves always interfere constructively are called
antinodes. (An antinode is a point of maximum displacement of the medium in a standing
wave.)
Note: The distance between any node and the adjacent antinode in a standing wave will
always be one-quarter of a wavelength. Since the air does not move at the bottom of the
PVC pipe, it makes sense that you will get a node to form at that point. The air is
vibrating by its greatest amount at a point just above the top of the PVC pipe so it makes
sense that an antinode forms there. Now when the length of the PVC pipe is properly
adjusted and the air inside the PVC pipe resonates, it is because the reflected sound wave
that is leaving the pipe is in-phase with the sound wave traveling down into the PVC
pipe. This is what produces the constructive interference that amplifies the sound. With
the length of the PVC pipe above water being just under ¼ of a wavelength, you might be
wondering how it is in phase. (If you look at the actual distance that the sound wave
traveled through the PVC pipe it is only about ½ of a wavelength. With the wave moving
a distance of ½ of the wavelength you might think that it should be out of phase and
produce destructive interference.) The answer is in what happens when a wave bounces
off a hard surface. When a wave is reflected off a hard surface, the wave gets inverted.
This inversion means that the wave acts as if it “jumped” ahead an additional half
wavelength. This means that as far as the wave moving through the PVC pipe is
concerned, it has effectively moved a distance equal to one full wavelength and that is
why it produces constructive interference when it combines with the next incoming sound
wave as it exits the PVC pipe.
If you are using the 523.3 Hz frequency tuning fork, you may notice that just as the
PVC pipe is being pulled all of the way out of the water, the sound appears to be getting
louder again. (The air in the PVC pipe is starting to resonate again.) This is because the
length of the pipe is approaching ¾ of the wavelength of the sound wave being produced
by the tuning fork. The shortest length of the pipe that will cause the air inside it to
resonate is about ¼ of a wavelength. (This does not take into account the end-correction
factor.) If the pipe length is increase by ½ wavelength intervals, it will also produce
resonance. You just need to remember that you need to have a node at the closed end and
an antinode at the open end and that the distance between nodes and antinodes are always
¼ of the wavelength apart.
When performing this lab you should hold the tuning fork about
an inch (about 2.5 cm) above the top of the PVC pipe. (See the
picture to the right.) This will not only keep it above the location
where the antinode will form, but it will reduce the chances of
your hitting the PVC pipe with the tuning fork.
It is important that you adjust the length of the PVC pipe to
find the point where the sound is the loudest. If it appears to you
that there is a range of positions where the sound is equally
loud, try to find the middle of that range. The length of the PVC
pipe above the water level at this point is critical. You must
make sure that the PVC pipe does not move from this location
until after you have time to measure the length of the pipe above
the surface level of the water.
I suggest that you lay the tuning fork
across the top of the PVC pipe to act as a
sight line to make it easier to read the
metrestick. The bottom of the metrestick
should be placed at the location of the
water level in the glass cylinder. The
height of the PVC pipe above the water
can be found by reading off the location
indicated by the bottom of the tuning fork.
(Note: you should stop the tuning fork
from vibrating before you lay it across the
top of the PVC pipe.) The measurements
for the length of the PVC pipe above the
water level and of the inside diameter of
the PVC pipe should be measured and
recorded to the nearest millimetre.
Note: it is important that you check the room’s air temperature each time you use a new
tuning fork. Depending upon the time of year and the number of times the door to the lab
gets opened, you may see changes of the air temperature in the lab. This will shift the
value of the “accepted” speed of sound. Your speed of sound based upon the calculated
wavelength of the sound wave and the frequency of the tuning fork will be used to obtain
the “measured” speed of sound. In this lab for each tuning fork you use where the
“measured” speed of sound and the “accepted” speed of sound differ by more than 2.0 %,
your grade will be reduced by 5 points.
If in addition to answering in general how you would use what is done in this lab to find
the frequency of an unmarked tuning fork you actually take the requirement
measurements and calculate the frequency of the supplied unmarked tuning fork to within
2% of the correct value, 5 points will be added to your lab grade for this lab.
You will be using an electronic thermometer (shown below) to measure the air
temperature. What you will find is that there is no “on/off” switch on it. The thermometer
will turn on automatically when the temperature probe is “opened up” and turn off when
the temperature probe is pushed back against the body of the thermometer.
Notes on using the thermometer:
You should remember that in the lab (unless I say otherwise) we will always be using SI
units. This means that the thermometer should be set to give the temperature in Celsius
degrees. (This is indicated in the picture above by the “c” showing up on the display.)
Since the thermometer is measuring the temperature of the probe, please do not handle
the probe any more than necessary. Every time that you touch the probe, you are
transferring thermal energy to the thermometer probe and throwing the temperature off.
You need to measure and the record the temperature each time that you take a reading of
the length of the PVC pipe above water. If the temperature in the room changes, it
changes the speed of sound in air.
Notes on using the tuning forks:
Never strike them on anything hard. If they are damaged in any way, it will change the
frequency at which they vibrate. You should always strike them on your knee to get them
started, and stop them from vibrating with your hand before you put them down.
Hold them at least an inch (2.5 cm) above the top of the PVC pipe when trying to get the
air inside the PVC pipe to resonate. (This will keep it above the location of the antinode
and help keep you from hitting the PVC pipe by accident as you move the pipe up and
down.)
Notes on the required calculations on data
In the calculations:
- the “measured” speed of sound is to be obtained by multiplying the frequency marked
on the tuning fork and the calculated wavelength of the sound wave produced.
- the “accepted” speed of sound is to be obtained by using the air temperature.
- the percent relative error is obtained by comparing the speed of sound based upon
frequency and wavelength with the speed of sound based upon the air temperature.
% relative error = |measured value - accepted value| x 100%
accepted value
Important: since the percent relative error is obtained by dividing the absolute value of
the difference between the two speeds of sound by the “accepted” speed of sound, it is
always going to be a positive number.