Lesson35.notebook
May 27, 2013
Unit 4 ­ Waves and Sound
Waves and Their Properties
Today's goal: I can explain the difference between transverse and longitudinal
waves and their properties.
Waves are a disturbances that transfer energy over a distance. The sources of
these disturbances occur from vibrations. For example:
­ Earthquakes cause the ground to vibrate.
­ A tuning fork's tines vibrate.
­ A plucked string on a guitar or a piano string vibrate.
The vibration source supplies the energy that is transferred through the medium
as a wave.
A medium is the same as saying "the composition or material" a wave is passing
through. It could be water, air, steel, wood, ...
There are two types of vibration.
Longitudinal vibration occurs when an object oscillates (moves back and forth)
parallel to its natural rest position.
Transverse vibration occurs when an object oscillates (moves back and forth)
perpendicular to its natural rest position.
General properties of vibrations:
A cycle is one complete oscillation of vibration. (ie. The object returns to its original
position in the oscillation.)
Frequency is the number of cycles per second. Formula:
Period is the time required for one cycle to occur. Formula:
The relationship between frequency and period is:
Lesson35.notebook
May 27, 2013
Transverse versus Longitudinal Vibrations
Lets use an example from a "real­life" experience to analyze.
Transverse Vibration
eg. The girl on the swing.
Longitudinal Vibration
eg. Mass on a hanging spring.
Lets analyze the girl on the swing or the Transverse vibration.
Lesson35.notebook
A better representation:
May 27, 2013
http://www.schulphysik.de/suren/Applets.html
Lets analyze the oscillating spring or the Longitudinal vibration.
Lesson35.notebook
A better representation:
May 27, 2013
http://www.schulphysik.de/suren/Applets.html
Example: Longitudinal vs Transverse
Sketch a wave with an amplitude of 10 units and a period of 12 seconds.
Lesson35.notebook
May 27, 2013
Drawing waves in 2 ­ D
Example: A mass hung from a spring vibrates 15 times in 12 seconds. Calculate:
A) The frequency.
B) The period of vibration.
Example: The frequency of a wave is 6.0 x 101 Hz. Calculate the period.
Example: A child on a swing has an amplitude of 1.2 m. What total distance does
the child move through horizontally in 3 cycles?
Lesson35.notebook
May 27, 2013
Universal Wave Equation
We know from kinematics that the velocity of an object in a constant state of motion
can be calculated by:
Now if we introduce some of our "new" terminology into the mix:
Example: Calculate the speed of sound leaving the tuning fork at a frequency of
125 Hz, if the wavelength of one cycle is 275 cm.
Example: Find the velocity of the wave if the wavelength is 75 cm and the period
is 2 minutes.
Homework:
page 473, #23 ­ 32
Lesson36.notebook
May 27, 2013
Transmission and Speed of Sound
Today's goal: I can explain how sound is transmitted through a medium and how
real­world applications (ie. Mach number) are connected with the concept.
Sound is a longitudinal wave which requires a medium to travel in. This would
mean that...
Sound is a form of energy transfer. In this situation we are transferring energy
created from vibration to "sound" energy. For the energy to travel it requires a
medium and the medium will determine the speed of sound.
Why?
We know from the kinetic molecular theory that...
Some examples of different mediums:
Medium
Density (kg/m3)
Air
1.29
Water
1000
Copper
8930
Iron
7800
Page 446 in textbook lists several other mediums.
Speed of sound (m/s)
331
1498
3800
5000
In general, the stiffer the material, the faster the speed of sound in the
medium.
Even within air itself, there will be a variance of velocity as with all materials, as the
temperature of the medium increases, the distance between particles increases
making the transmission of energy less efficient. A simple class example:
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The relationship:
Through experimentation physicists have determined that the temperature affects
the velocity of sound in air by 0.6 m/s /C. Therefore:
v = 332 + 0.6T,
where:
Example: Find the velocity of sound in air when the mean temperature is 30
degrees Celsius.
Example: If you see a lightning strike and then 5 seconds later you hear the
thunder, determine how far away the lightning was if the temperature this evening
is 18 degrees Celsius.
Lesson36.notebook
May 27, 2013
What is SONAR?
­ SOund Navigation And Ranging
Bats and dolphins use this to determine how far they are from an
object. They emit sounds at a high rate (130kHz range). These waves
bounce off any objects which they happen to come into contact with. By
seeing how long it takes for the wave to come back to them they can
determine how far the object is.
The Mach Number
The "Mach Number" is simply a comparison of velocity with respect to the velocity
of sound in air under current conditions.
For example, if the temperature is 0 degrees Celsius then,
Mach 1 = 332 m/s
Mach 2 = 2 x 332
Mach 3 = 3 x 332
= 664 m/s
= 996 m/s
Example: Determine the Mach Number of a plane flying at 850 m/s in an air
temperature of 5 degrees Celsius.
Lesson36.notebook
Example: A plane is travelling at Mach 1.8 or 500 m/s. What is the air
temperature?
Homework
3U Page 474, #33 ­ 48
May 27, 2013
Lesson37.notebook
May 27, 2013
The Sound Barrier
Today's goal: I can explain phenomena like the sound barrier, sound intensity and
the Doppler effect work using proper terminology.
The term "sound barrier" describes the build up of sound waves in front of a fast
moving object. This happens as the object's speed increases and begins to
"catch" its own sound waves.
Stationary Object
Moving Object
Fast moving object
As an object reaches the sound barrier (approx. 332 m/s) there is an enormous
pressure buildup as the air particles have been compressed very close together.
In order to break through this pressure barrier an large amount of energy is
required.
The aviation industry never had a shortage of energy, however, maintaining
control was a major issue. Most planes that reached the sound barrier were not
able to be controlled. Not until the advent of the "delta wing" or "sweep wing"
design was the sound barrier safely crossed.
The Sonic Boom
The "sonic boom" or "sonic shock wave" is the result of an object travelling faster
than the speed of sound and leaving a "pressure wake" behind it. The wake
spreads out similar to the wake of a boat until it reaches ground level for the
observer.
http://www.explorelearning.com/index.cfm?method=cUser.dspLoginJoin
Lesson37.notebook
May 27, 2013
The four stages:
v = 0 m/s
v = mach 1
v < mach 1
v > mach 1
Sound Intensity
Similar to water waves dissipating as they move away from a source (dropped
pebble) so do sound waves.
The intensity (I) of a sound wave is defined as the rate of power (P) that passes
through an area (A) perpendicular to the wave's direction.
Therefore,
I=P/A
Comparing Two intensities:
however in the "real­world" is 3­D so:
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May 27, 2013
Sound is measured using the Decibel System which works in magnitudes of
millions for each range. To make the numbers manageable and also result in a
linear relationship, physicists use "logarithms" to analyze sound intensity.
Just a bit of grade 12 math to help put things in perspective:
β = 10log(I1)
Δβ = 10log(I1/I2)
Example: Given a sound source's intensity is 5.0 x 10­6 W/m2 determine the
intensity if:
A) The distance from the source is doubled.
B) The distance from the source is quartered.
Example: How many times more intense is a motorcycle (100 dB) than a passing
train (70 dB)?
Lesson37.notebook
May 27, 2013
Example: A passing train produces sound at 70 dB measured 3 m away. How far
must you stand so that the sound level is 50 dB?
The Doppler Effect
The Doppler Effect is a physical phenomena that everybody has experienced at one
point or another in their lifetime. The following slides introduce and discuss the
topic.
Case 1: The sound is moving toward you.
f2 = frequency heard
f1 ‐ frequency from horn
vs ‐velocity of sound
vo ‐ velocity of object
Lesson37.notebook
May 27, 2013
Case 2: The sound is moving away from you.
f1 ‐ frequency from horn
vs ‐velocity of sound
vo ‐ velocity of object
f2 = frequency heard
Example: A taxi is approaching Dylan at a velocity of 20 m/s while honking its
horn. Calculate the frequency of the sound heard by Dylan if the horn has a
frequency of 500 Hz and the speed of sound is 344 m/s when:
A) The taxi is approaching Dylan.
B) The taxi is driving away from Dylan.
Homework:
page 475
#49, 56 ­ 58, 61, 62, 64 ­ 71
Lesson38.notebook
May 27, 2013
Sound Waves and Matter
Today's goal: I can explain how sound waves are absorbed, transmitted and/or
reflected through matter and apply the knowledge to different situations.
All forms of waves can be absorbed, transmitted or reflected.
Absorption
Absorption is the process where sound's energy is quickly dissipated by being
transformed into other forms of energy.
Engineers have accomplished this by using absorptive materials (cork, heavy
cloth, etc...) and odd looking 3­D "baffles" that reflect the sound until the waves
get absorbed.
Example: Wall cross ­ section
Transmission
Transmission is the passing of sound energy from one medium to another at the
medium boundary.
Using a ratio of velocity for each medium and the Universal Wave equation we find
that:
Lesson38.notebook
May 27, 2013
Example: A sound wave travelling through air (v = 332 m/s) and with wavelength of
0.75 metres hits a steel wall. What is the wavelength that is transmitted into the
steel wall if speed of sound in steel is 5000 m/s?
Reflection
Sound energy can hit a surface and be reflected back onto itself. However, the
reflected wave has its phase shifted by 1/2λ. There are two types of reflection:
http://www.schulphysik.de/suren/Applets.html
Fixed End Reflection
Free End Reflection
Lesson38.notebook
Waves at a boundary (ex. Air to Steel)
Homework:
page 512 #13
May 27, 2013
Lesson39.notebook
May 27, 2013
The Principle of Superposition
Today's goal: I can explain and apply the concept of superposition in terms of
wave interference and predict the resulting
destructive interference.
http://www.schulphysik.de/suren/Applets.html
When you performed the "wave property" investigation you saw in some of you
results "dark" or "black" lines created. For example:
Interference
Constructive Interference ­ Multiple waves are in a cycle which enhances
the amplitude of the crest or trough.
Destructive Interference ­ Multiple waves are in a cycle which decreases
the amplitude of a crest or trough.
Lesson39.notebook
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Lesson39.notebook
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Homework:
Complete the handout
May 27, 2013
Lesson40.notebook
May 27, 2013
Characteristics of Sound
Today's goal: I can explain the various characteristics of sound and apply them to
real­world phenomena (ie. beat frequency, nodes, etc...).
An oscilloscope transforms sound energy to a graphical representation of the
wave. Example:
Frequency and Sound
Amplitude and Sound
Interference and Beats
When two waves with different frequencies result in both constructive and destructive
interference it creates "beats".
A "beat" is a full cycle of loudness.
Graphing Calculator:
y=5sin(30πx)
Tuning Forks:
Beat Frequency is |f2 ­ f1| and fbeats = N / Δt
Lesson40.notebook
May 27, 2013
Example: When a tuning fork with a frequency of 512 Hz and a tuning fork of
unknown frequency are heard together for a period of 4 seconds there are 20
beats. What is the possible frequency of the second tuning fork?
Standing Waves
A standing wave occurs when a wave reflects back on itself with the
same frequency, wave length and speed. The resulting wave has a
particular pattern caused by a special kind of interference.
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May 27, 2013
reflected wave
wave
Calculating Internodal Distance
dn = (1/2)λ
Example: A standing wave occurs in a duck pond when a duck repeatedly tries to jump
for food.
A) If there are nodes at every 38 cm, what wavelength of wave is the duck creating?
B) If the wave speed in the pond is 0.95 m/s, how often is the duck jumping?
Lesson40.notebook
May 27, 2013
Resonance
Every object is vibrating at a particular frequency. This is called the objects
natural frequency.
Frequency
Diagram
Physic Term
Music Term
Mechanical resonance is the vibrating response of an object to a periodic force from
a source that has the same frequency as the natural frequency as the natural
frequency of the object.
Example: The Tuning Forks
Lesson40.notebook
Real ­ Life Application: The Tacoma Narrows Bridge
Less "disastrous" examples of resonance:
1) Rocking a car when stuck in the snow.
2) Pushing a child on a swing.
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Lesson40.notebook
3) The baseball bat
Homework:
page 512 #17, 18
page 514 #37 ­ 39
May 27, 2013
Lesson41.notebook
May 27, 2013
Acoustical Resonance
Today's goal: I can explain concepts of acoustical resonance, specifically, how it
applies to open and closed ended air columns.
Acoustical Resonance is the process responsible for sound waves that come from
various instruments, each tuned to a particular natural frequency. When played a
standing wave is created or "played".
Wind instruments are elaborate air columns in which a standing wave is formed.
For example:
Open ­ Ended
Closed ­ Ended
Using a chart we can investigate the general properties of open and closed air
columns:
`
Open ended instrument:
Resonant
Length
Diagram
Number of Length of column in
terms of wavelength
nodes
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May 27, 2013
Closed ended instrument:
`
Resonant
Length
Diagram
Number of
nodes
Length of
column in terms
of wavelength
Example: An air column that is open at both ends is 1.5 m long. A specific
frequency is heard. If the air temperature is 20 degrees C, what is the longest
possible wavelength and its frequency to cause resonance?
Lesson41.notebook
May 27, 2013
Example: A closed air column resonantes at two consecutive lengths (fundamental
frequencies) of 94 cm and 156 cm. If the air temperature is 20 degrees C,
determine the resonant frequency of the air column.
Homework:
page 512 #19 ­ 26
Lesson42.notebook
May 27, 2013
Woodwinds and Stringed Instruments
Today's goal: I can explain how various wind and stringed instruments work
using concepts discussed in the unit using proper terminology.
Recall:
Open ­ Ended:
L=
Closed ­ Ended:
L=
If velocity remains constant and we apply the universal wave equation:
Frequency
Wavelength
Pitch
With air columns, we have to keep the frequency constant so:
Length of column
The Trombone
Pitch
Lesson42.notebook
May 27, 2013
The Flute
The Guitar
Four variables affect the frequency of a string with stringed instruments:
1) Length:
Inversely proportional ­
2) Tension:
Directly proportional ­
(square root)
3) Diameter: Inversely proportional ­
4) Density:
Inversely proportional ­
(square root)
Lesson42.notebook
May 27, 2013
Example: A guitar player changes the string length from 0.9 m to 0.4 m. It has a
new frequency of 500 Hz. Determine the original frequency.
Example: Determine the resulting frequency if the string on a guitar is changed
such that the heavier wire is used (density and diameter are doubled), the length
is 10% shorter, the tension is tripled.
Homework:
The handout