Vibrations & Waves
Chapter 25 - Thiswill be phun!
2 Types of Waves
Mechanical Wave:
Requires a mechanical medium
Sound, water, air, springs, or ropes are examples.
Electromagnetic Waves (EM):
Does not require a medium for motion to occur
Light, Radio, and X-rays are examples.
“Making Waves”
Transverse Waves
Causes the particlesof the medium tovibrateperpendicularly tothe direction ofmotion of the wave.
Piano and guitarstrings areexamples
Longitudinal Waves
When particles ofthe medium moveparallel to thedirection of thewaves.
Fluids, liquids,gases, or plasmausually transmit onlylongitudinal waves.
Longitudinal and Transverse
Longitudinal vs TransverseWaves
Compression = Crest
Rarefaction = Trough
Energy Movement:
parallel vs perpendicular
Wavelength:
compression + rarefaction
crest + trough
Surface Waves
They are a mixture of transverse andlongitudinal waves. (water & Rayleigh)
The particles move both parallel andperpendicular to the direction of the wave.
Wave Pulse and Traveling Wave
Wave Pulse:
A single disturbance that travels through amedium.
Traveling Wave:
Moving, periodic disturbances in a medium or field.
Period
The shortest timeinterval during whichthe motion repeatsitself.
Abbreviated with thecapital letter,T
SI Unit: seconds (s)
Frequency
The number of completerevolutions per second.
Frequency isabbreviated with a fancyƒ.
Frequency is measuredin Hertz, Hz.
A Hertz is one vibrationper second (1/s).
Equation
Frequency and the period of a wave arerelated by the following equation.
Frequency and Period are reciprocals ofeach other.
Wavelength
The shortest distancebetween points wherethe wave pattern repeatsitself.
The wavelength isabbreviated with theGreek letter, lambda,
A: ?
B: ?
C: ?
D: ?
E: ?
Wavelength
The shortest distancebetween points wherethe wave pattern repeatsitself.
The wavelength isabbreviated with theGreek letter, lambda,
A: 1 Wavelength
B: 2X Amplitude
C: Nodes
D: Amplitude
E: ½ Wavelength
Vocabulary
Crests:
The high points of each wavemotion.
Troughs:
The low points of each wavemotion
Amplitude:
The maximum displacementfrom the rest or equilibriumposition.
Nodes:
Where the wave crosses theequilibrium line.
Antinodes:
The bottom of the trough andthe top of the crest
Vocabulary
Crests:
The high points of each wavemotion.
Troughs:
The low points of each wavemotion
Amplitude:
The maximum displacementfrom the rest or equilibriumposition.
Nodes:
Where the wave crosses theequilibrium line.
Antinodes:
The bottom of the trough andthe top of the crest
A&F: Crests (Antinodes)
D&I: Troughs (Antinodes)
B,E,G,J: Nodes
To find the velocity of a wave
Wave velocity (v) is the product of thefrequency (f) and wavelength ().
To find out how fast a wave moves, youwould use this equation…
Amplitude and Energy
In order to produce awave with a largeramplitude, moreenergy is needed.
Waves with largeramplitudes transfermore energy.
Amplitude does notaffect frequency norvelocity.
Waves Changing Mediums
Waves passing from one medium toanother have the same frequency.
The wavelength change depends on thevelocity change so that f is constant.
If the velocity increases, the wavelengthincreases (direct relationship).
Superposition and Interference
Principle ofSuperposition:
Two or more wavesoccupying the samespace.
Interference:
The result from twoor more wavesoccupying the samespace.
Constructive Interference
Occurs when the wavedisplacements are inphase (crest meetscrest or trough meetstrough).
The result is a wavewith a larger amplitudethan the individualwaves.
Destructive Interference
Occurs when the wavedisplacements are out ofphase (crest meetstrough).
The result is a wave witha smaller amplitude thanthe individual waves.
Red: wave moving right
Blue: wave moving left
Green: superposition
(Red + Blue wave)
Destructive Interference
If the pulses haveunequal amplitudes,destructive interferenceis not complete. Thepulse of the overlap isthe algebraic sum of thetwo pulses.
Red: wave moving right
Blue: wave moving left
Green: superposition
(Red + Blue wave)
Standing Wave
When the nodes and antinodes arestationary, the wave appears to bestanding still.
If you increase the frequency of astanding wave, you will see morenodes.
Superposition of Waves
A. Two pulses traveling in opposite directions
B. Two sine waves traveling in the samedirection, but at different speeds
C. Two sine waves traveling in oppositedirections.
Nodes and Antinodes
Node:
The point in the medium that is completely undisturbed atall times. A node is produced by destructive interferenceof waves
Antinode:
The point of maximum displacement. An antinode isformed from constructive interference.
Harmonics
Let’s check for understanding…
The number of nodesin the standing waveshown in the diagramat the right is
a.6
b.7
c.8
d.14
Let’s check for understanding…
The number of nodesin the standing waveshown in the diagramat the right is
c.8
Let’s check for understanding…
The number ofantinodes in thestanding wave shownin the diagram at theright is
a.6
b.7
c.8
d.14
Let’s check for understanding…
The number ofantinodes in thestanding wave shownin the diagram at theright is
b.7
Let’s check for understanding…
In the standing wave shown,
a. What is the amplitude?
b. What is its wavelength?
c. How many nodes are there?
d. How many antinodes are there?
Let’s check for understanding…
In the standing wave shown,
a. What is the amplitude? 10 cm
b. What is its wavelength?
c. How many nodes are there?
d. How many antinodes are there?
Let’s check for understanding…
In the standing wave shown,
a. What is the amplitude? 10 cm
b. What is its wavelength? 1 m
c. How many nodes are there?
d. How many antinodes are there?
Let’s check for understanding…
In the standing wave shown,
a. What is the amplitude? 10 cm
b. What is its wavelength? 1 m
c. How many nodes are there? 6
d. How many antinodes are there?
Let’s check for understanding…
In the standing wave shown,
a. What is the amplitude? 10 cm
b. What is its wavelength? 1 m
c. How many nodes are there? 6
d. How many antinodes are there? 5
Reflection of Waves
Normal:
A line that is drawnperpendicular to thebarrier (green).
Angle of Incidence:
The angle between theincidence ray and thenormal.
Angle of Reflection:
The angle between thenormal and the reflectedray.
>I = >R
Refraction of Waves
Refraction:
The changein thedirection ofwaves at theboundarybetween twodifferentmedia.
Diffraction of Waves
Diffraction:
The spreading ofwaves around theedge of a barrier.
Diffraction occurswhen waves meet asmall obstacle.
They can bendaround the obstacle,producing wavesbehind it.
Problem-Solving
Springs
Spring Constant
Spring Constant (stiffness)
A spring stretches 18 centimeters when a 56Newton weight is suspended from it. What isthe spring constant?
Find: k
Givens: d (x) = 18 cm = 0.18 m
F = 56 N
Formula: k = F
d
Solution: 310 N/m
Springs
Potential Energy in aSpring
Period of a Pendulum
Pendulum
Using a Pendulum
A pendulum with a length of 36.9 centimetershas a period of 1.22 seconds. What is theacceleration due to gravity at the pendulum’slocation?
Find: a (g)
Givens: d = 36.9 cm = 0.369 m
T = 1.22 s
Formula: g = 42L
T2
Solution: 9.78 m/s2
Velocity, Wavelength, Frequencyand Period Relationships
Wavelength
Wavelength
An 855 Hertz disturbance moves through aniron rail at a speed of 5130 meters persecond. What is the wavelength of thedisturbance?
Find:
Givens: f = 855 Hz
v = 5130 m/s
Formula: = v
f
Solution: 6.00 m
Velocity, Wavelength, Frequencyand Period Relationships
Period
Period
An 855 Hertz disturbance moves through aniron rail at a speed of 5130 meters persecond. What is the period of thedisturbance?
Find: T
Givens: f = 855 Hz
Formula: T = 1
f
Solution: 0.00117 s
Velocity, Wavelength, Frequencyand Period Relationships
Velocity
Velocity
A sound wave has a frequency of 192 Hertzand travels the length of a football field, 91.4meters, in 0.271 seconds. What is the speedof the wave?
Find: v
Givens: f = 192 Hz
d = 91.4 m
t = 0.271 s
Formula: v = d
t
Solution: 337 m/s
Velocity
A sonar signal of frequency 1.00 X 106 Hertzhas a wavelength of 1.50 millimeters in water.What is the speed of the signal?
Find: v
Givens: f = 1.00 X 106 Hz
= 1.50 mm = 0.00150 m
Formula: v = f
Solution: 1.50 X 103 m/s
