Vibrations and
Waves
Vibrations and Waves
“Wiggles in Time”
“Wiggles in Space”
 Oar in Water
 Water Waves
 Wings of a Bee
 Sound Waves
 Electrons in an
 Light Waves
Light Bulb
Vibrations and Waves
 Waves transmit energy and information.
 Sound and Light are both waves.
Simple Harmonic Motion...
 …is to-and-fro vibratory motion.
 ...results in sine curves.
 Examples:



metronome
mass on a spring
pendulum
Forces and vibrations
 Vibration - repetitive back




and forth motion
At the equilibrium position,
spring is not compressed
When disturbed from
equilibrium position,
restoring force acts toward
equilibrium
Carried by inertia past
equilibrium to other extreme
Example of “simple harmonic
motion”
Describing vibrations
 Amplitude - maximum extent




of displacement from
equilibrium
Cycle - one complete
vibration
Period - time for one cycle
Frequency - number of
cycles per second (units =
hertz, Hz)
Period and frequency
inversely related
Description
 Period - the time required for one vibration

measured in seconds
 Frequency - number of vibrations per unit time

measured in Hertz
Bowling Ball Example
1
Period 
Frequency
1
Frequency 
Period
Bowling Ball Example
Pendulums & Galileo
 The period does not depend on the amount of
mass.
 The period does depend on the length of the
pendulum.
T  2 l g
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Example Test Question:
If you double the frequency of a vibrating
object, what happens to the period?
a) the period doubles
b) the period stays the same
c) the period is cut in half
d) not enough information is given
to answer this question.
Example Question
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Changing which of the following affects the
period of a pendulum?




a) mass
b) amplitude
c) length
d) angle
What is the frequency in vibrations
per second of a 60-Hz wave?
Answer: 60 cycles per second
What is its period?
Answer: 1/60 second
Waves
 Periodic (traveling) disturbances transporting energy
 Causes
 Periodic motion disturbing surroundings
 Pulse disturbance of short duration
 Mechanical waves
 Require medium for propagation
 Waves move through medium
 Medium remains in place
Wave Motion
 medium - the stuff that carries the wave
Waves
Medium
water waves
water
waves on a rope
rope
stadium waves
people
sound
air
light
space (vacuum)
Wave Speed...
 the speed with which waves pass by a
particular point

e.g. the speed of a surfer
 It depends only on the type of medium.
 Wave Speed = Frequency  Wavelength
Waves on a Rope
Table in Notes – Appearance, Node, Antinodes, Wavelength, Frequency
Describing waves
Graphical representation
 Pure harmonic waves =
sines or cosines
Wave terminology
 Wavelength
 Amplitude
 Frequency
 Period
Wave propagation speed
Example Test Questions
Answer these questions using the sine wave provided.
1. What is the amplitude of the wave?
2. What is its wavelength?
3. How many nodes are there?
Example Wave
2 ½ meters
20 cm
Wavelength = 1 m
Amplitude = 10 cm
Number of Nodes = 6
If a water wave oscillated up and down three
times each second and the distance
between wave crest is 2 m, what is its
frequency?
Answer: 3 Hz
What is its period?
Answer: 1/3 second
What is its wavelength?
Answer: 2 m
What is its wave speed?
Answer: 6 m/s
Kinds of waves, cont.
Transverse waves
 Vibration direction perpendicular to
wave propagation direction
 Example: plucked string
Solids - support both longitudinal and
transverse waves
Surface water waves
 Combination of both
 Particle motion = circular
Kinds of waves
Longitudinal waves
 Vibration direction parallel to wave
propagation direction
 Particles in medium move closer
together/farther apart
 Example: sound waves
 Gases and liquids - support only
longitudinal waves
Waves in air
 Longitudinal waves only
 Large scale - swinging door
creates macroscopic
currents
 Small scale - tuning fork
creates sound waves
 Series of condensations
(overpressures) and
rarefactions
(underpressures)
INTERFERENCE
 Constructive or destructive interference
results when waves add.
 Standing Waves - wave pattern produced
from interfering waves

Examples



Vibrating Strings in Lab
Organ Pipe in Lab
Bell Wave Machine in Class
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
DOPPLER EFFECT
 the change in wavelength due to motion of
the source
 "Wheeeeeeeeeeee…….Oooooooooooooo”
 Examples:
 moving cars and trains
 moving buzzer in a nerf ball (in class)
 rotating whistle
Draw Doppler Picture
Sounds from moving sources
 Doppler effect
 Wave pattern changed by
motion of source or observer
 Approaching - shifted to
higher frequency
 Receding - shifted to lower
frequency
 Supersonic speed - shock
wave and sonic boom
produced
http://www.kettering.edu/~drussell/Demos/doppler/doppler.html
Question 1
*
A train whistle at rest has a frequency of 3000
Hertz. If you are standing still and observe the
frequency to be 3010 Hertz, then you can
conclude that...




a) the train is moving away from you.
b) the train is moving toward you
c) the sound from the whistle has echoed
d) not enough information is given
Question 2
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Dipping a finger in water faster and faster
causes the wavelength of the spreading
waves to




a) increase
b) decrease
c) stay the same
d) not enough information is given
Question 3
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The distance from trough to trough on a
periodic wave is called its...




a) frequency.
b) period.
c) wavelength.
d) amplitude.
Sound...
...a longitudinal wave in air caused by a
vibrating object.
 Sound requires a medium.


solid, liquid or gas
Sound waves have compression and
rarefaction regions.
Nature of Sound in Air
 Sound requires a medium.

solid, liquid or gas

Demo: Bell in a evacuated Bell Jar
 Sound waves have compression and
rarefaction regions.
Sound
 infrasonic
 frequencies < 20 Hz
 ultrasonic
 frequencies > 20,000 Hz
 human hearing range
 frequencies between 20 Hz and 20,000 Hz
Sound waves
 Require medium for
transmission
 Speed varies with



Inertia of molecules
Interaction strength
Temperature
 Various speeds of
sound
Velocity of sound in air
 Varies with temperature
 Warmer the air, greater the kinetic energy of the gas
molecules


Molecules of warmer air transmit sound impulses from
molecule to molecule more rapidly
Greater kinetic energy sound impulse transmitted
faster
 Increase factor (units!):
0.6 m/s/°C;
2.0 ft/s/°C
SPEED OF SOUND
How it varies:
increases with humidity
increases with temperature
increases with density
Lightning and Thunder
What is the approximate distance of a
thunderstorm when you note a 3 second delay
between the flash of the lightning and the
sound of the thunder?
Answer: 3 seconds  340 meters/second
= 1020 meters
See blue questions on page 345.
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Sources of sound




Vibrating objects
Source of all sound
Irregular, chaotic vibration produces noise
Regular, controlled vibration can produce
music
 All sound is a combination of pure
frequencies
Vibrating strings
 Important concepts - strings with fixed ends



More than one wave can be present at the
same time
Waves reflected and inverted at end points
Interference occurs between incoming and
reflected waves
Vibrating strings, cont.
 Standing waves
 Produced by interferences at
resonant frequencies
 Nodes - destructive
interference points
 Anti-nodes - points of
constructive interference
Resonant frequencies of strings
 Fundamental - lowest
v
fn = n
2L
frequency
 Higher modes - overtones
(first, second, …)
 Mixture of fundamental and
overtones produces “sound
quality” of instrument
 Formula for resonant
frequencies