PHYS 103Report 3 InstructionsSound and ResonanceDownload thi.docx

PHYS 103
Report 3 Instructions
Sound and Resonance
Download this document and record the results in the table
below as prompted by the procedure. Save the completed
document to your computer and upload it via the provided
assignment link. All photos and discussion must be submitted
within a single 1–2-page Word document.
Take a picture of the setup at the prompt in the assignment with
a visible white piece of paper labeled with your name and date.
The data table below must be completed in its entirety. Submit
photo of the table and show all of your work.
Submit Report 3 by 11:59 p.m. (ET) on Monday of
Module/Week 5.
Sound and Resonance
Carolina Distance Learning
Investigation Manual
2

©2015 Carolina Biological Supply Company
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

3
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

resonance
Time Requirements
Preparation
...............................................................................................
5 minutes
Activity 1
...............................................................................................
..10 minutes

4
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.
5

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).
6
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.
� = (0.5�)(27 ��)
� = 13.5 �/�
Waves exhibit many phenomena:
7

example of this is
waves bending when passing through a gap, such as ocean
waves passing
between barrier islands.
e 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.
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.
8

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.
9
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.
10
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.
�� = 331.4 + 0.6��
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.
11

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:

�� = 331.4 + 0.6��
v = fλ
% �� = |
�� − ��
(
�� + ��
2
)
| � 100%
12
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.

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