LAB 3
Sound and Resonance Carolina Distance Learning
Investigation Manual
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Table of Contents
Overview……………………………………………………………………………………. 3
Objectives …………………………………………………………………………………………. 3
Time Requirements ……………………………………………………………………………. 3
Background ………………………………………………………………………………………. 4
Materials ……………………………………………………………………………………………. 9
Safety ………………………………………………………………………………………………. 10
Preparation ……………………………………………………………………………………… 10
Activity: Standing wave in a tube open at one end ………………………. 10
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Overview
In this activity, students will use a tuning fork to generate standing waves in a tube that
is open at one end and identify the length of tube necessary for the sound of the tuning
fork to be amplified through resonance, which is an increase in the amplitude of a
wave at a specific frequency. Through an understanding of the properties of waves
and the conditions necessary to establish standing waves in this scenario, students will
calculate the speed of sound in air at room temperature and the wavelength of sound
generated by the tuning fork.
Objectives
Develop an understanding of the properties of waves
Calculate the speed of sound in air at room temperature
Generate a standing wave and demonstrate the property of resonance
Time Requirements
Preparation …………………………………………………………………………………..5 minutes
Activity 1 …………………………………………………………………………………….10 minutes
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Background
Waves can transmit energy over a great distance. Seismic waves generated by
earthquakes can cause extensive damage; scientists use their knowledge of seismic
waves to locate the epicenter of an earthquake. Sound and light are transmitted
through waves. Waves can also carry complex information over a long distance, for
example, radio waves. Some radios can send and receive complex signals and
broadcast over great distances. In this activity you will calculate the speed of sound in
air and apply some basic knowledge of waves to determine the wavelength of sound
generated by a tuning fork.
A wave is a propagation of energy due to a rhythmic disturbance in a medium or
through space. A medium is the material through which a wave travels. Mechanical
waves, such as waves in water, can only travel through a medium composed of some
form of matter. Sound waves are mechanical and can travel through a gas, such as
the air in earth’s atmosphere, liquid, and solid matter, but not through a vacuum.
Electromagnetic waves can travel through a medium, such as light waves through
glass, or through the vacuum of space, such as a radio signal.
A mechanical wave is transmitted when the molecules of a medium, such as air or
water, move or vibrate in a repeating or oscillating motion. The particles of the medium
generally remain in their original positions and vibrate back and forth, but the energy of
the wave travels outward from the wave source.
Mechanical waves can be classified as transverse or longitudinal. In a transverse wave
the particles of the medium move or vibrate in a direction that is perpendicular to the
direction of the wave. A group of people performing “the wave” in a stadium is a good
example of a transverse wave. People move their arms up and down (vertically), and
the wave travels horizontally around the stadium. When a string on a musical
instrument, such as a guitar or piano, is plucked or struck, the molecules in the strings
vibrate in one direction, whereas the energy in the wave travels along the length of the
string.
Sound travels in a longitudinal wave, also called a compression wave. When a sound
wave is generated, the molecules of the medium vibrate in a direction parallel to the
direction of the wave, but do not travel with the wave, remaining in the same location.
When a sound is generated, e.g., by the tuning fork in this activity, the air near the
source vibrates, causing a disturbance in the surrounding air molecules that travels
outward in all directions, but the air molecules near the source and along the wave
generally remain in their original locations.
Longitudinal mechanical waves travel through solids, liquids, and gases; however
transverse waves only travel through solid or liquid matter.
The intensity and frequency of a wave are functions of the wave source, whereas the
speed of the wave is determined by the medium through which the wave travels. To
better understand waves, consider the diagram in Figure F1.
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Figure F1.
The horizontal line is called the rest position. This is where the particles in the medium
rest until disturbed by the energy from the wave. The distance labeled A is the
amplitude of the wave. The amplitude of the wave is directly related to the intensity, or
acoustic energy, of the sound. For a sound wave, greater amplitude means louder
sound. The amplitude is the distance from the rest position to the position of greatest
displacement. The position of greatest displacement above the rest position, the
highest point on the wave, is the crest. The position of greatest displacement below the
rest position is the trough. The wave height (WH) is twice the amplitude. The distance
between any two identical points (i.e., two crests or two troughs) on a waveform is the wavelength and is represented by the Greek letter lambda (λ). In depictions of
waveforms the wavelength is usually depicted between two crests, as in Figure F1.
The waveform in Figure F1 can represent any kind of wave. The amplitude and
wavelength provide enough information to analyze the wave. You may have seen
sound waves represented by this type of waveform on an oscilloscope or computer
screen.
In a sound wave, which is a compression wave, the air molecules move together in
regions called compressions, and spread apart in regions called rarefactions (Figure F2).
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Figure F2.
Another important property of waves is frequency. The frequency is the rate at which
the particles in the medium vibrate. Frequency is measured in Hertz (Hz; cycles per
second, cycles/s, cycles × s-1). Try tapping an object, such as a pencil, on a surface, such
as a table, at a rate of one tap per second. That is a frequency of 1 Hz. The inverse of
wave frequency is the period of the wave. If you tap the pencil at a frequency of 2 Hz
or two taps per second, the period, or time between taps is 0.5 s. What is the highest
frequency at which you can tap the pencil? The tuning fork in this kit has a frequency of
2048 Hz. Humans can hear sounds in a frequency range of 20–20,000 Hz. Anything above
the range of human hearing is called ultrasound, and anything below is called
infrasound. A dog whistle makes an ultrasonic sound that is too high for humans to hear,
but within the audible range for dogs. As people age, the ability to hear the higher
frequencies diminishes.
The velocity, or speed, of a wave is related to the wavelength and frequency as
described in the equation:
v = fλ
where v is velocity in meters/s; f is frequency in Hz, and λ is wavelength measured in
meters.
For example, consider a wave with a wavelength of 0.5 m and a frequency of 27 Hz.
𝒗 = (0.5𝑚)(27 𝐻𝑧)
𝒗 = 13.5 𝑚/𝑠
Waves exhibit many phenomena:
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Echo Waves reflect off solid objects.
Diffraction Waves diffract, or bend, around solid objects. An example of this is
waves bending when passing through a gap, such as ocean waves passing
between barrier islands.
Interference Waves interact with other waves. Imagine two instruments, such as
trumpets, that are slightly out of tune, or have a slightly different pitch. Both
trumpets play the same note, but the wave forms leaving each instrument are
out of sync. The result is an oscillation in the intensity or loudness of the sound.
Two sound waves result in a tone that has “beats” of higher and lower volume.
Standing waves: At certain frequencies, a wave source may create waves that
reflect back from one end of a medium and interfere with waves emanating
from the source. A wave pattern is established where every point on the wave
has a constant amplitude. A simple demonstration of a standing wave can be
created with a rope or string. Tie a rope to a post or other immovable object.
Pull the rope tight and then move it rhythmically up and down. Vary the speed
of movement until the rope generates a constant wave form similar to that
shown in Figure 4. The wave pulses travel from the wave source, your hand, to
the post and reflect back. At a particular frequency, the wave appears to stand
still. In this example, the frequency depends on the linear density of the rope
(mass per unit length; g/cm) and the tension. If you are having trouble setting up
a standing wave with a rope, try adjusting the tension.
Where the wave forms cross, there is no displacement of the rope. These points
are called nodes. The rope is maximally displaced halfway between two nodes.
These points are called antinodes. Because you are moving the rope at one
end, that end is an antinode. The end at which the rope is anchored is a node.
Try changing the frequency of the wave. Each new frequency will be
associated with a different standing wave pattern, with different numbers of
nodes and antinodes. These frequencies and the associated wave patterns are
called harmonics.
Figure F3 shows how standing waves are established in an air column in a tube
that is open at both ends. Each harmonic is an integral multiple of the first
harmonic, or fundamental frequency. If the velocity of air is known and the
length of the column can be measured, the frequency of each harmonic can
be calculated.
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Figure F3.
Figure F4 shows how standing waves are established in a tube that is closed at
one end. There will be a node at the closed end of the tube and an antinode at
the open end. Whenever the frequency of the wave is an odd-numbered
integral of the fundamental frequency, a standing wave will be established in
the tube.
Figure F4.
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Materials
Included in the Sound and Resonance kit:
Tuning fork, 2048 Hz
Plastic tube, open at both ends
Needed from the Central Materials set:
Graduated cylinder, 2 parts, unassembled
Ruler, metric
Needed, but not supplied:
Calculator
Permanent marker
Reorder Information: Replacement supplies for the Sound and Resonance investigation
can be ordered from Carolina Biological Supply Company, kit 580406.
Call 1-800-334-5551 to order.
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Safety
Read all instructions for this laboratory activity before beginning. Follow the
instructions closely and observe established laboratory safety practices, including
the use of appropriate personal protective equipment (PPE) described in the Safety
and Procedure sections.
Do not eat, drink, or chew gum while performing this activity. Wash your hands with
soap and water before and after performing the activity. Clean up the work area
with soap and water after completing the investigation. Keep pets and children
away from lab materials and equipment.
Preparation
1. Go to a quiet location with enough workspace to place the graduated cylinder on
a flat surface. Strike the tuning fork against your hand and hold it at arm’s length. If
you cannot hear the tuning fork, move to a quieter location.
2. Use your ruler and permanent marker to mark the entire length of the clear plastic
tube at 1-cm intervals. Allow time to dry.
In the following activity you will measure the speed of sound in air. Using the tuning fork
as a sound source and a tube, one end of which is submerged in water in a graduate
cylinder, you will adjust the length of the air column in the tube until a standing wave is
established. When the standing wave is set up, the tube will resonate, which amplifies
the sound slightly. You will then be able to calculate the wavelength of the standing
wave.
Activity: Standing wave in a tube open at one end
1. Calculate the speed of sound in the surrounding atmosphere. Measure the
temperature of the room using the thermometer, and use the following equation.
𝑣𝑠 = 331.4 + 0.6𝑇𝐶
where vs = the speed of sound in meters per second (m/s), 331.4 m/s is the speed of
sound in air at freezing temperatures, and Tc = the temperature of the room in
degrees Celsius. 0.6 is a constant with dimensions of, m/s/°C.
Record TC and vs values in the Data Table.
2. Assemble the graduated cylinder by placing the cylinder in the base.
3. Fill the graduated cylinder to the top with water.
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4. Place the plastic tube in the cylinder. The submerged end is the closed end of the
resonance tube, and the end above the surface of the water is the open end.
5. Strike the tuning fork on the palm of your hand or a book and hold the vibrating
tuning fork about 2 cm (~¾ in) above the mouth of the plastic tube.
6. Raise the plastic tube, increasing the length of the air column in the tube, while
keeping the tuning fork about 2 cm above the mouth of the tube.
7. Listen for the point at which the plastic tube amplifies the sound from the tuning fork.
It may be necessary to strike the tuning fork again during the experiment if the
sound becomes too faint, and it may be necessary to move the tube up and down
to reach to find the exact point where the sound from the tuning fork is amplified.
8. Measure the distance from the open end of the tube to the water. This is the length
of ¼ of one wavelength. Record this value (L1) in Data Table.
9. Continue moving the tube upward, further extending the length of the air column,
until you reach the next point where the sound from the tuning fork is amplified. This
is the length of ¾ of one wavelength. (See Figure 6) Record this value (L2) in Data
Table.
10. Move the tube upward again until you reach the next point where the sound from
the tuning fork is amplified. This is the length of 5/4 of one wavelength. Record this
value (L3) in Data Table.
11. Complete Data Table, using the speed of sound in the air (vs) to calculate the
length of the wavelength, λ.
12. Calculate the percent difference between the values you calculated for the
speed of sound using the closed tube and the equation from step 1 using the
equation:
𝑣𝑠 = 331.4 + 0.6𝑇𝐶 v = fλ
% 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = | 𝑓𝑖𝑟𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 − 𝑠𝑒𝑐𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒
( 𝑓𝑖𝑟𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 + 𝑠𝑒𝑐𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒
2 )
| 𝑥 100%
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Figure 6
Data Table
Temperature
(°C)
vs*
(m/s)
f
(Hz)
Length (L)
(m)¶
Calculate
λ§
(m)
Vs**
(m/s)
2048
L1
(L1=λ/4 and λ=4L1)
L2
(L2=3λ/4 and λ=4L2/3)
L3
(L3=5λ/4 and λ=4L3/5)
*Speed of sound in air (vs) = 331.4 + 0.6TC.
**Speed of Sound in air (vs) = fλ ¶Convert cm measurements to m. §Using equation vs = fλ and/or λ = vs/f.