N Dae Hyun Bae
Chapter 19
Vibration and Waves
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Good Vibrations
o A vibration is a periodic “wiggle” in time
o This periodic “wiggle” in both space and time is called a wave and it extends from one
place to another
 Ex. Light which is an electromagnetic wave
 Ex. Sound which is a mechanical wave through some kind of a medium
Vibration of a Pendulum
o If u suspend a stone at the end of a string, u get a simple pendulum
o The pendulum swings at a rate that depends on:
 Only the length of the pendulum
 Not upon the mass (because the mass does not affect the rate at which a ball
falls to the ground)

The equation for this is called the Pendulum Vibration Formula: T = 2π√
o
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𝐿
𝑔
A Period is the time it takes to make a full swing
 The longer the length of the pendulum, the larger the period
Wave Description
o A Sine Curve is way to pictorially represent a wave
 A Sine Curve is obtained by tracing out the path of a vibrating pendulum over a
certain period of time
𝑚
o
The Spring-Mass Equation: T = 2π√ 𝑘
o
Some of the Vibration and Wave characteristics
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Amplitude Equation:
|𝑀−𝑚|
2
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o
Crest
 The highest point of a wave
 Trough
 The lowest point of a wave
How frequently a vibration occurs is called frequency

Equation for frequency is:

1
1
𝑔
f = 𝑇 and f = 2𝜋 √ 𝐿
Unit for frequency is Hertz (Hz) after a guy named Heinrich Hertz
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 A frequency of 1 Hz is a vibration that occurs once each second
 Mechanical objects such as pendulums have frequencies of several Hz
 Sound has a frequency between 100 and 1000 Hz
 Radio waves have frequency of several million Hz (MHz)
 Cell Phone operates at frequencies of several billion Hz (BHz)
 Frequency specifies the number of full cycle vibrations in a given time
o Period is inversely proportional to frequency
Wave Motion
o Wave Motion
 Waves transport energy and not matter
 Ex. Dropping a stone in a serene pond would result in ripples which do
not carry water across the pond, but rather vibrates, moving away and
then back, basically transferring energy
 Ex. Waves travel across grass on a windy day
o Wave Speed
 It describes how fast a disturbance moves through a medium
 Relates to frequency and wavelength of a wave
 Equation of wave speed: 𝑊𝑎𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ∗ 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
 How do u get the equation?
𝑑
: Speed = 𝑇
: Wave Speed =
𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
𝑝𝑒𝑟𝑖𝑜𝑑
: V = λ𝑓
: 𝑊𝑎𝑣𝑒 𝑆𝑝𝑒𝑒𝑑 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 ∗ 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ
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Transverse and Longitudinal Waves
o Longitudinal Wave

o Transverse Wave
 Wave that vibrates from side to side
 The vibration occurs perpendicular to the direction of the energy transfer
 Ex. Radio Waves
 Ex. Light Waves
 Ex. S – Waves
Wave Interference
o Wave Interference
 It occurs when two or more waves interact with each other due to an overlap of
occurrence in the same place and the same time
 Constructive Interference
 Occurs when the crest of one wave overlaps the crest of another
 The individual effects add together to produce a wave that is increased
in amplitude
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Destructive Interference
 Occurs when the crest of one wave overlaps the trough of another wave
 The high part of once wave fills in the low part of the other wave
o Thus, reduction of the amplitude or cancelation occurs
 Ex. The interference pattern made when two vibrating objects touch the surface
of water
 Ex. When waves arrive out of step, it is called Out of Phase
o Superposition Principle
 States that the displacement due to the interference of waves is
determined by adding the disturbances produced by each wave
Standing Waves
o By shaking the rope just right, you can cause the incident and reflected waves to form
things called Standing Waves
o A Node is the point in which there is no displacement
 Nodes divide / make the distinction between the periods
o An Antinode is the point which has maximum displacement
o Antinodes and nodes happen equally apart from each other
2𝐿
𝑛
o
Equation:
o
Harmony is when wavelength goes perfectly between nodes
 L = whole length from beginning to end
Ex. Sound waves in trumpets
Ex.2 Wave of a guitar string
Doppler Effect
 From a moving sound source
 When the moving sound source is moving towards the person, the
waves have short wavelengths and are more frequent
 When the moving sound source is moving away from the person, the
waves have long wavelengths, and are less frequent
 Also applies to light
 There is an Increase in light frequency when the light source approaches
you
 There is a decrease in light frequency when the light source goes away
from you
 Doppler effect of light
 Blue Shift
o Increase in light frequency towards the blue end of the
spectrum
 Red Shift
o Decrease in light frequency towards the red end of the
spectrum
o
o
o
𝑾𝒂𝒗𝒆𝒍𝒆𝒏𝒕𝒉 =
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Bow Waves
o Supersonic
 Aircrafts flying faster than the speed of sound
o Bow Wave
 V-shape form of overlapping waves when objects travel faster than wave speed
 An increase in speed will produce a narrower V-shape of the overlapping waves
Shock Waves
o Shock Wave
 Consists of two cones
 A high pressure cone generated at the bow of the supersonic aircraft
 A low pressure cone that follows toward or at the tail of the aircraft
o Sonic Boom
 Sharp cracking sound generated by a supersonic aircraft
 Intensity due to overpressure and under pressure of atmosphere pressure
between the two cones of the shock waves
 Produced before it brakes the sound barrier
 Ex. Supersonic bullet
 Ex. 2 Crack of a circuit whip
Question: Why do you need to use 120 not 220 volts?
o It is safer to use 120 volts, but it is more efficient to use 240 volts.
Question: Why do you need to use 60Hz not 50Hz
o It is 20 percent more effective and 10-50 percent more efficient to use the 60Hz than
the 50Hz, due to that fact that the 50Hz electric generators are slower in speed and
because they require larger windings.