PHY124
Lab # 1
Sound and Waves
Name ___________________
Introduction
From first semester physics we learn that work is a measure of what is being
accomplished. We put a number to the amount of work done by looking at two things…
the amount of force being applied and the displacement that that force acts through.
Work = (force)(displacement)
Energy is the ability to do work. Any time that work is being done energy is being used.
There is more than one form of energy (gravitational potential energy, elastic potential
energy, kinetic energy and others) and more than one way to transfer energy from one
place to another. We can use a wave to transfer energy from one place to another with no
net transfer of matter.
Mechanical waves are a physical displacement of an elastic medium that transfers
energy with no net transfer of matter. (Note: the term medium refers to the material that
the wave is traveling through.) A longitudinal wave will cause the medium to vibrate
back and forth along the same line of action as the direction that the energy is traveling
in. When the medium is vibrating in a direction that is at right angles to the direction that
the energy is traveling in, the wave is called a transverse wave. (An example of a
transverse wave is a water wave. If you throw a rock in a pond, the ripples formed will
cause the water to move up and down as the energy in the wave travels out in larger and
larger circles from the point where the rock entered the water.)
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
What follows is an outline of the things that the instructor will be doing.
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Part A
Basic wave motion
1) Using a long spring, show how mechanical waves can transfer energy without a net
transfer of matter.
2) Explain the concept of a “reflected” wave.
3) Discuss and demonstrate the interference pattern that develops when two waves of the
same frequency pass through the same spot in opposite directions. Introduce the terms
“constructive” and “destructive” interference, “resonance” and “standing waves”.
4) Define the following terms:
Periodic motion (use a pendulum and a weight a spring)
Wavelength
Frequency
Period
Velocity (speed = frequency * wavelength)
Speed of sound in air (v = 331 m/s + 0.6 Tc)
Amplitude
Transverse wave
Interference
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A mechanical wave can be described as a physical disturbance in an elastic medium
that transmits energy with no net displacement of matter. To demonstrate how energy can
be transferred without having to move matter, a long spring will be run across the front of
the physics lab with one end tied in place and the other end held by the instructor. When
the instructor quickly moves the end of the spring off to the side and then back it will
generate a pulse that will travel down the length of the spring. As the energy in this pulse
travels down the spring it will cause each part of the spring to temporarily move sideways
and then return to its original location. When this pulse gets to the location of the water
bottle sitting on the floor, the spring will knock it over. Since it takes energy to do the
work required to move the bottle, it should be obvious that energy was being transferred
from where the instructor was to where the bottle was. The thing is… once the pulse
passes through a given part of the spring it returns to its original location. This means that
we have indeed transferred energy without having a net transfer of matter.
Also important in this demonstration is the fact that when the pulse got to the end of the
spring it did not simply stop. Instead it reflected off the object that the end of the spring
that was tied in place and then returned. Note: any time that a wave hits a hard object
and reflects off, the wave will get inverted. This is why the wave went down with the
pulse on right-hand side, but it returned on the left-hand side.
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.)
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In the diagram to the right the two speakers are
producing the same frequency note in phase with
each other. (The first is shown in blue and the
other in green.) At the moment in time shown, the
two waves interfere constructively at all points
and the resultant wave (shown in red) is larger
than the one produced by either one of the two
waves alone.
At the point in time shown to the right, which is
one-quarter of a cycle later, the two speakers are
still producing the same note in phase, but at
every point in between the two speakers the two
sound waves interfere destructively and the result
is that they cancel each other out everywhere.
In the diagram shown to the right, which is onehalf of a cycle after the top diagram, the speakers
again produce sound waves that interfere
constructively with each other.
Note: even though the two waves are interfering
constructively, there are points where the air
pressure is still at standard atmospheric pressure.
At these locations the air pressure never changes
because of the two waves passing by.
What you will find is that there are certain points between the two sound sources where
the air pressure never changes. The locations are called nodes. A node is a point of no
displacement of the medium. At the points located between the nodes, the medium will
vibrate at its maximum amounts. These locations in a standing wave are called antinodes.
In the diagram shown to the right
the location of the nodes are
shown with the letter N and the
locations of the antinodes are
shown with the letter A.
It should be noted that the distance between any node and the adjacent antinode will
always be equal to ¼ of the wavelength of the sound wave.
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Part B
Sound waves
1) Using the suspended spring explain and demonstrate the differences between a
longitudinal wave and a transverse wave.
2) Explain the basic operation of a typical speaker.
3) Using the oscilloscope, let the students see and here the sound coming from a sine
wave generator.
Note: An oscilloscope is a device that allows us to get a visual representation of an
electrical signal. The oscilloscope generates a tiny beam of electrons that scan across the
face of the display. When the electron beam strikes the coating on the inside front surface
of the display it causes a brief glow at the location where the electrons hit. As the beam is
moved across the display, it “paints” a line that shows where the beam struck. This beam
starts out on the left hand side of the screen and moves across the face of the display at a
constant rate that can be adjusted using the controls on the front of the oscilloscope. As
the input voltage is increased, the beam is shifted up towards the top of the display. When
the input voltage is decreased, the beam is shifted down towards the bottom of the
display. This means when looking at the display of an oscilloscope you represent voltages
by looking at how tall the trace on the display is, and you read time based upon horizontal
motion across the surface of the display. In the pictures below, a sound level meter is
used as a microphone to convert the changes in air pressure into a varying electrical
signal being fed into the oscilloscope so that you can “see” the changes in air pressure
and a computer is used to generate three different sounds that are sent to the speakers
connected to the computer.
In this first picture to the right the display shows what
a 440 Hz sound “looks” like. It shows that a “pure tone”
(as from a tuning fork) causes the air pressure to change
over time in a manner that looks like a standard sine
wave.
In the second picture the same note is played at a
larger volume. Increasing how “loud” a sound is
increases the amount of the variation in air pressure, but
does not change the frequency. (You get the same
number of cycles completed each second because the
air is still vibrating at a rate of 440 Hz.)
In the third picture the frequency generated by the
computer is changed to 880 Hz. As a result of doubling
the frequency you get twice as many cycles being
completed each second. Therefore you get twice as
many cycles showing up on the screen.
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4) Explain the following terms: (For the definitions of the terms, see the glossary below.)
Pitch (in terms of frequency)
Loudness (in terms of amplitude)
Octave (a doubling of the frequency)
Part C
Speed of Sound
1) Explain the relationship between the speed of sound in air and air temperature.
m
m
v  331  0.6 s Tc 
s
C
2) Explain the relationship between the speed of a wave, the frequency of the wave and
the wavelength.
vf λ
Part D
Interference
1) Use the tuning forks, a large glass cylinder and a section of PVC pipe to get a column
of air to resonate. (Mention how they will be doing the same thing in the speed of sound
lab.)
2) Remind them of what constructive and destructive interference are explain how the
materials can be used this way to create a mechanical sound amplifier.
3) Change the frequency of the tuning fork to demonstrate the relationship between the
length of the PVC pipe and the frequency that will cause the air inside the pipe to
resonate.
4) Using the adjustable frequency tuning forks demonstrate “sympathetic” vibration and
discuss the term “beat” frequency.
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Glossary of Terms to know
Amplitude – refers to maximum displacement away from the equilibrium position for
some object that moves with periodic motion.
Beat Frequency – refers to increase and decrease in volume that occurs when two
different (but close) sound waves are played at the same time. The rate at which the
amplitude of the resulting sound varies will be equal to the simple difference between the
frequencies of the two sound waves that are interfering with each other. As an example if
two notes are played at the same time and the first has a frequency of 256 Hz and the
second has a frequency of 257 Hz, then they will switch between interfering
constructively and interfering destructively once per second. (Note: the beat frequency
can be found as follows: 257Hz – 256 Hz = 1 Hz.)
Cycle – a complete set of changes in the position (or condition) of some object before its
motion starts to repeat itself. Note: the object undergoing this periodic motion must not
only be back in its starting position, but the full range of motions must all be repeated in
order for it to have completed one full cycle.
Frequency (f) – a measure of the number of times some motion repeats itself per unit
time. Typically measured in Hertz, which is equivalent to a cycle per second. We tend to
use frequency for describing how often something repeats itself when it repeats itself
many times per second. Note: frequency of something is equivalent to the reciprocal of
its period.
Interference – A term used to describe what happens when two waves try to pass
through the same point at the same time. If both waves are trying to get the medium to
move/vibrate in the same direction, then the combined effect is such that the medium will
move more than it would due to just one of these waves passing through at a time. This is
referred to as constructive interference. When sound waves interfere constructively, that
is… when they are both trying to cause the air pressure to increase and decrease at a
certain point in space at the same time, the end result is that the air pressure varies more
than it would if only one of these waves were present. Constructive interference with
sound waves leads to what we interpret as an increase in volume. (Sounds get louder with
constructive interference.)
Longitudinal Wave – is a type of wave where the medium (that is the material that is
actually vibrating as the energy in the wave moves) is vibrating back and forth along the
same line of action as the direction that the energy in the wave is moving in. Note: sound
waves are examples of longitudinal waves because as the sound waves travel through the
air, it causes the air to vibrate alternately towards and away from the source of the sound
as the sound waves travel away from the source of the sound.
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Loudness – A term that is typically used to describe the relative amplitude of the sound
waves. As a sound gets “louder”, the variations in air pressure (that is the amplitude of
the sound waves) increase. As a sound wave gets “softer”, the variations in air pressure
decrease.
Octave – A term that is used to refer to a doubling in frequencies of a sound wave. When
you change from one C to the next musical note that is also called a C, the frequency of
the “higher” note will be exactly double the frequency of the lower note. If you select a
certain note and then play another note that is two octaves higher, the higher note will
have four times the frequency of the first. (Each time the musical note increases by
another octave, the frequency doubles again.)
Period – The length of time it takes for an object that undergoes periodic motion to
complete one full cycle. The period of some motion is typically used when the length of
time it takes to complete one cycle is longer than a second. Note: period and frequency
are reciprocals of each other.
Periodic Motion – A term that describes any motion that repeats itself in equal intervals
of time.
Pitch – A term used in music to refer to the (fundamental) frequency of a sound.
Transverse wave - is a type of wave where the medium (that is the material that is
actually vibrating as the energy in the wave moves) is vibrating back and forth at right
angles with respect to the direction of the energy flow for the wave. Note: water waves
are examples of transverse waves. If you throw a rock into a pond, you can watch the
surface of the water move up and down as the circular ripples move outward away from
the place where the rock entered the water.
Wavelength (λ) – the distance that a wave moves as it completes one cycle. (It really is,
in essence, the length of the wave.)
Important Equations to know:
Beat Frequency (f1 – f2)
Speed of sound in air (v = 331 m/s + 0.6 Tc)
Velocity (speed = frequency * wavelength; v  f λ )
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