T H E P H Y S I I C S O F
W A V E S
S O U N D : :
W A V E S – T H E S E Q U E L ( ( P A R T I I I I ) )
C o n c e p t s C o v e r r e d i i n t t h i i s P a c k a g e : :
U n i i v e r s a l l W a v e E q u a t t i o n , , E f f f f e c t t s o f f F r e q u e n c y a n d
W a v e l l e n g t t h o n S o u n d , , P h a s e s , , I I n t t e r f f e r e n c e , , R e s o n a n c e
O N W O R K
I
I N G W
I
I
T
H N A T U R E
’
’
S C Y C L E
S .
.
.
.
.
.
Unit: Sound and Waves
Waves Part Two: More on Waves
1

T h e U n i i v e r s a l l W a v e E q u a t t i i o n
Simple waves possess various qualities, including the wave’s
F R E Q U E N C Y
, which is the number of times it cycles per second and is its W A V E L E N G T H , which is the distance from any point on the wave to its corresponding point in the next cycle.
The graph below illustrates both:
Fig. 1: Wavelength
Wavelength (λ) = If the wave requires one second to complete the distance, then the frequency ( f) = 1 cycle per second (1 Hz). The wavelength can be microscopic or huge.
Scientists usually measure them metrically, such as millimetres, meters or kilometres.
Unit: Sound and Waves
Waves Part Two: More on Waves
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This provides everything we need to use the U N I I V E R S A L W A V E E Q U A T I I O N
, a simple formula that we can apply to all waves. The equation is as follows:
T H E U N I I V E R S A L W A V E E Q U A T I I O N : :
V = f f
.
.
λ
V = v e l l o c i i t y ( ( s p e e d ) ) o f f t t h e w a v e f f
= t h e f f r r e q u e n c y o f t h e w a v e *
λ = t t h e w a v e l l e n g t h
* O n e w a y t t o m e a s u r e f f r r e q u e n c y i i s c y c l l e s p e r s e c o n d , , o r r h e r t t z .
.
The Universal Wave Equation:
V = f
.λ
0 1 2 3
Frequency = cycles per second
Figure 2
Unit: Sound and Waves
Waves Part Two: More on Waves
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T e s t t y o u r k n o w l l e d g e !
!
A s s u m i i n g t t h a t t t t h e s p e e d o f f s o u n d r e m a i i n s c o n s t t a n t t , , u s e t t h e U N I I V E R S A L W A V E E Q U A T I I O N t t o a n s w e r r t t h e f f o l l l l o w i i n g q u e s t t i i o n s .
.
1.
W h a t t h a p p e n s t t o t t h e f f r r e q u e n c y ( ( t t h e n u m b e r r o f f h e r r t t z o r r f f u l l l l c y c l l e s p e r s e c o n d ) ) i i f f t t h e w a v e l l e n g t t h d e c r r e a s e s ?




I I t t i i n c r r e a s e s
I I t t d e c r e a s e s
2.
W h a t t h a p p e n s t t o t t h e f f r r e q u e n c y i i f f t t h e w a v e l l e n g t t h i i n c r r e a s e s ?
I I t t i n c r r e a s e s
I I t t d e c r e a s e s
S o , , h o w d o e s f f r r e q u e n c y a f f f f e c t t t t h e s o u n d t t h a t t w e h e a r r ?
?
T h e h i i g h e r r t t h e f f r r e q u e n c y , , t t h e h i i g h e r r t t h e p i i t t c h !
!
*Check your answers. Correct answers located on last page.
Unit: Sound and Waves
Waves Part Two: More on Waves
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P i i t t c h i i s A f f f f e c t t e d b y F r r e q u e n c y -
R e a l l l l i i f f e E x a m p l l e
“Aboriginal musicians have learned to adjust a finished drum to maintain the deep, resonant tones they desire. The membrane’s tension and thickness
(weight) determine the natural frequency at which it vibrates, but other variables also affect the way it sounds. The problem is that temperature and humidity stretch or shrink the membrane, which changes its pitch. Cool, moist weather causes both the hide and the pitch to become loose and limp. Hot, dry weather stretches it too tightly, making the sound high-pitched and tinny.
“To offset these effects, a drummer will heat or cool the drum’s membrane before playing. If the hide is wet and flabby, the musician will hold the drum over a fire or use a heater or hair dryer, which causes the membrane’s pores to contract. It the hide is dry and tight, the drummer will brush in drops of water to loosen the skin and lower the tone.”
“ “ S e c r r e t t s o f f S o u n d , , ” ” A n d r e w T r r a c y , , N a t t i i v e D r r u m s W e b s i i t t e
T h e P h a s e o f f a W a v e
0°
90°
180
°
360°
0° / 360°
270°
Figure 3 – Phases of a Wave
90°
270°
180
°
Unit: Sound and Waves
Waves Part Two: More on Waves
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Thus pictured, the graph allows us to place two or more waves on top of one another, which shows the PHASE DIFFERENCES between them. Phase differences create interference, which is among the most important qualities that create musical sound
Unit: Sound and Waves
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I I n t t e r f f e r e n c e
Sound waves are complex and interact in interesting ways.
T HE SUPERPOSITION OF
OSCILLATIONS describes what happens when two waves of different amplitudes pass through each other while keeping their respective shapes. When these two waves meet, they produce an audible effect, INTERFERENCE , which is the outcome of combining their amplitudes and waveforms.
Interference is important in music. So are overtones , the fact vibrating bodies produce harmonious additional sounds that are multiples of their lowest
(fundamental) frequencies. Exact multiples produce the harmonics without which rich and complex music would be impossible. Overtones are any higher frequency modes that are not necessarily harmonics . W ithout these interactions and effects sine waves and their simple single-note tones would be all we would hear. For example, if they existed, a single-note sine-wave flute would sound exactly like a single-note sine-wave mouth harp.
In other words, wave actions and interactions equal individuality. These effects combine to create music’s richness, variety and character.
Let’s look more closely at interference. As we will see in the next section, interference affects loudness.
Sound Becomes Increasingly Loud When . . .
The example below shows what happens when we blend two equally-loud waves that have the same frequency and are in step (in phase) with each other. The crests and troughs of the first wave will coincide with the crests and troughs of
Unit: Sound and Waves
Waves Part Two: More on Waves
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the second wave. This makes the combined wave’s amplitude double. We call this
C O M P L E T E C O N S T R U C T I I V E I I N T E R F E R E N C E
.
But, doubling the amplitude does not double the loudness because our ears are logarithmic sound detectors, the math of which is beyond this lesson’s scope. It would, however, make the sound noticeably louder, about six decibels or so.
E DITOR
’
S NOTE : P LEASE KEEP THE BLACK , RED AND GREEN COLOUR SCHEME .
Fig. 4 – Complete Constructive Interference
Wave 1 and wave 2 Have a 0° Phase Difference Between Them
+
Wave 2
+ =
If the crests and troughs of one wave coincide with the crests and troughs of another, the amplitude will double, and thus, the volume will be louder.
Unit: Sound and Waves
Waves Part Two: More on Waves
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S o u n d C e a s e s W h e n .
.
.
.
.
.
C O M P L E T E D E S T R U C T I V E I I N T E R F E R E N C E
Fig. 5 – Complete Destructive Interference
Wave 1 and Wave 2 Have a Phase Difference of 180°
Complete Destructive Interference
The amplitude at the crest of wave 1 CANCELS the amplitude at the trough of wave 2 . The resulting net amplitude of zero means no sound.
(Remember, the bigger the amplitude, the louder the sound! So, no amplitude, no sound!)
Wave 2
Wave 1 Crest
Wave 2 Trough
S o .
.
.
.
.
.
.
.
Interference’s two forms have opposite effects: Constructive interference increases a sound’s volume, while destructive interference decreases volume or even silences it completely.
Unit: Sound and Waves
Waves Part Two: More on Waves
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R
E S O N A N C E
As we can see from our discussion above, to amplify its sounds, the musician’s instrument must achieve
C O N S T R U C T I I V E I I N T E R F E R E N C E .
To more fully understand what this means, we need to explore the phenomenon of
R E S O N A N C E .
If a body that is already vibrating at its natural frequency* is again acted upon from the outside by a periodic disturbance* that matches its natural frequency or frequencies, then this can produce vibrations of ever increasing amplitude.
This phenomenon is R E S O N A N C E .
*Natural Frequency/Frequencies: The frequency or frequencies at which a body will vibrate at when someone plucks it, strikes it, drops it, or otherwise disturbs it. Physical properties, such as elasticity, mass, length, determine natural frequencies
*Examples of “outside periodic disturbances”: A drummer beating on a drum, a guitarist strumming on a guitar string, etc.
A N E X A M P L E O F R E S O N A N C E : :
In physics, a common example is an adult pushing a child on a swing.
Each time the swing goes up (or, to use physics jargon, the amplitude of its displacement increases). At the peak, gravity pulls it back down again.
The swing moves backward past its equilibrium position, hits an opposite high point and begins moving forward again. If the adult pushes at precisely the right moment, and if the push is stronger than all counteracting forces, the swing keeps going higher and higher. Some youngsters want Papa to push them all the way over the top bar, but we know better!
This reinforcement is resonance. This synchronized movement in a vibrating system is in phase when the pusher moves in the same direction
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as the movement. Technically, in-phase motion is a fraction of a completed cycle as reckoned from a chosen starting point. This is how musical instruments, such as violins and guitars, make the strings sound louder. Without resonance and acoustic coupling, we would barely hear a guitar’s strings or a drum beat. The effect combines with the way an instrument’s large surface area transfers its vibrations to the air. In a violin, the sound box and the air inside the instrument’s body resonates with the string. The same is true for drums.
Vibrations must be synchronized to obtain resonance in a musical instrument. When they are, we say the two resonating forces are in phase with one another, as we discussed earlier in this module.
“The Aboriginal way also seeks in-phase resonance, but of another kind.
When to hunt, when to create new life, when to live and when to die; all these require careful timing. We must learn to co-exist in harmony with the cycles of Earth, community and family. This often needs the Elder’s wisdom, one who has experienced the interdependence of many cycles.
Like the child’s swing, the drum and the vibrating string, to work with
Nature’s cycles at the right moment strengthens life’s power; to work against Nature diminishes or even cancels it.”
Clealls (Dr. John Medicine Horse Kelly), “Secrets of Sound,” Native Drums
Website)
Unit: Sound and Waves
Waves Part Two: More on Waves
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T e s t t t Y o u r r U n d e r r s t t t a n d i i i n g o n “ “ “ W a v e s – A n I I I n t t t r r o d u c t t t i i i o n .
.
.
” ” ”
* * * T T o r r r e e a a d d m o r r r e e a a b b o o u u t t t t t t h h e e s s c c i i i e e n n c c e e o o f f f s s o o u u n n d d , , , v v i i i s s i i i t t t “ “ “ S S e e c c r r r e e t t t s s o o f f f S S o o u u n n d d ” ” ” o o n n t t t h h e e N a a t t t i i i v v e e
D r r r u u m s s W e e b b s s i i i t t t e e .
.
.
1.
Constructive Interference, results in a sound of ___________ volume.

Increased

Decreased
2.
Destructive Interference: Waves have a phase difference of ________.


0°
360°

180°

None of the above
3.
If the crest of the first wave coincides with the trough of the second, the two waves will ___________________ at the point of interference; this is called complete destructive interference.

Result in increased volume

Cancel each other out at the point of interference

None of the above
4.
Complete Destructive Interference results in sound ______________ .


Ceasing
Increasing

Becoming fainter
5.
Considering what you have learned about constructive and destructive interference, what should the musician strive to achieve on his or her instrument?

Constructive Interference
Unit: Sound and Waves
Waves Part Two: More on Waves
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
Destructive Interference
6.
“Resonance” is an example of constructive interference.


True
False
*Check your answers. Correct answers located on last page.
Suggested Reading:
“ ABORIGINAL MUSIC AND PHYSICS ,” BY C LEALLS (D R .
J OHN M EDICINE H ORSE K ELLY ) AND
A NDREW T RACY , “S ECRETS OF S OUND ,” N ATIVE D RUMS W EBSITE
Unit: Sound and Waves
Waves Part Two: More on Waves
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ANSWERS
Using the Universal Wave Equation Questions
1.
The frequency INCREASES if the wavelength decreases.
2.
The frequency DECREASES if the wavelength increases.
*Remember : The higher the frequency, the higher the pitch!
Other Questions (at the end of package)
1.
Increased volume
2.
180 degrees
3.
Cancel each other out at the point of interference
4.
Ceasing
5.
Constructive interference
6.
True
Unit: Sound and Waves
Waves Part Two: More on Waves
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