Lesson 22
Vibrations and Waves
Eleanor Roosevelt High School
Chin-Sung Lin
Vibrations and Waves
What is Vibrations?
What is Vibrations?
Vibrations
 Vibration: A wiggle in time
is a vibration
 A vibration cannot exist in
one instant, but needs
time to move back and
forth
 Mechanical oscillations
about an equilibrium point
Vibrations
 Period (T): The amount of time required for a
vibrating particle to return to its original position
(one cycle). A complete back-and-forth vibration is
one cycle. The unit of period is second (s)
Vibrations
 Frequency (f): The number of back-and-forth
vibrations it makes in a given time. The unit of
frequency is called hertz (Hz). One Hz is one cycle or
vibration per second
Frequency
 Frequency unit:
 1 kilohertz (kHz— thousands of hertz) = 1 x 103 Hz
 1 megahertz (MHz— millions of hertz) = 1 x 106 Hz
 1 gigahertz (GHz— billions of hertz) = 1 x 109 Hz
 frequency = 1/period and period = 1/frequency
f = 1/T
and
T = 1/f
Frequency Example
 If an electromagnetic wave has frequency 5.0 x
106 Hz, what is the period of the wave? What
type of wave is that?
Frequency Example
 If an electromagnetic wave has period 2.0 x 109 s, what is the frequency of the wave? What
type of wave is that?
Frequency
 High frequency and low frequency
What is Wave?
Waves
 sound waves
 stadium waves
 light waves
 earthquake waves
 radio waves
 rope waves
 microwaves
 slinky waves
 water waves
Waves
 Wave: A wiggle in space
and time is a wave
 A wave cannot exist in one
place, but must extend
from one place to another
 Disturbances that transfer
energy from one place to
another
Waves
 Crest and Trough: The high points of a wave
are called crests, and the low points of a wave
are called troughs
Waves
 Amplitude (A): refers to the distance from the
midpoint to the crest (or trough) of the wave. So the
amplitude equals the maximum displacement from
equilibrium
Waves
 Wavelength (λ): The distance between successive
identical parts of the wave such as from the top of
one crest to the top of the next one
Waves
Wavelength
Crest
Amplitude
Distance
Wave
Trough
Period
Amplitude
Vibration
Time
Aim: Speed of Waves
DoNow:
 Non-digital clocks have a second hand that rotates
around in a regular and repeating fashion. The
frequency of rotation of a second hand on a clock is
_______ Hz
 An echo (reflection of the scream off a nearby
canyon wall) is heard 0.82 seconds after the scream.
The speed of the sound wave in air is 342 m/s.
Calculate the distance from the person to the nearby
canyon wall
Aim: Speed of Waves
DoNow:
 Non-digital clocks have a second hand that rotates
around in a regular and repeating fashion. The
frequency of rotation of a second hand on a clock is
__1/60__ Hz
 An echo (reflection of the scream off a nearby
canyon wall) is heard 0.82 seconds after the scream.
The speed of the sound wave in air is 342 m/s.
Calculate the distance from the person to the nearby
canyon wall __ 140 m__
Speed of Waves
Waves
 wave speed = wavelength x frequency
= wavelength / period
v=
f=
/T
where v is the wave speed [m/s]
is the wavelength [m]
f is the wave frequency [Hz]
T is the wave period [s]
 This relationship holds for all kinds of waves
Waves
 The long wavelengths have low frequencies; the
shorter wavelengths have higher frequencies
 Wavelength and frequency vary inversely to produce
the same speed for all waves
Wave Example
 The time required for the sound waves (v = 340 m/s)
to travel from the 512-Hz tuning fork to 20 m away is?
Wave Example
 The time required for the sound waves (v = 340 m/s)
to travel from the 512-Hz tuning fork to 20 m away is?
[0.059 s]
Wave Example
 Mac and Tosh are resting on top of the water near the
end of the pool when Mac creates a surface wave. The
wave travels the length of the pool and back in 25
seconds. The pool is 25 meters long. Determine the
speed of the wave.
Wave Example
 Mac and Tosh are resting on top of the water near the
end of the pool when Mac creates a surface wave. The
wave travels the length of the pool and back in 25
seconds. The pool is 25 meters long. Determine the
speed of the wave.
[2 m/s]
Wave Example
 The water waves travel at a speed of 2.5 m/s and
splashing periodically against Wilbert's perch. Each
adjacent crest is 5 meters apart. The crests splash
Wilbert's feet upon reaching his perch. How much
time passes between each successive drenching?
Wave Example
 The water waves travel at a speed of 2.5 m/s and
splashing periodically against Wilbert's perch. Each
adjacent crest is 5 meters apart. The crests splash
Wilbert's feet upon reaching his perch. How much
time passes between each successive drenching?
[2 s]
Wave Example
 A ruby-throated hummingbird beats its wings at a rate
of about 70 wing beats per second. (a) What is the
frequency in Hertz of the sound wave? (b) Assuming
the sound wave moves with a velocity of 350 m/s,
what is the wavelength of the wave?
Wave Example
 A ruby-throated hummingbird beats its wings at a rate
of about 70 wing beats per second. (a) What is the
frequency in Hertz of the sound wave? (b) Assuming
the sound wave moves with a velocity of 350 m/s,
what is the wavelength of the wave?
(a) [70 Hz]
(b) [5 m]
Wave Example
Two boats are anchored 4 meters apart. They bob
up and down, returning to the same up position
every 3 seconds. When one is up the other is
down. There are never any wave crests between
the boats. Calculate the speed of the waves.
32
Wave Example
Two boats are anchored 4 meters apart. They bob
up and down, returning to the same up position
every 3 seconds. When one is up the other is
down. There are never any wave crests between
the boats. Calculate the speed of the waves.
[2.667 ms]
Wave Example
 If an electromagnetic wave has period 4.0 x 10-15 s,
what is the frequency of the wave? What is the
wavelength of the wave? Which type of wave is that?
Aim: Types of Waves
DoNow:
 If an electromagnetic wave has period 4.0 x 10-15 s,
what is the frequency of the wave? What is the
wavelength of the wave? Which type of wave is that?
Aim: Types of Waves
DoNow:
 If an electromagnetic wave has period 4.0 x 10-15 s,
what is the frequency of the wave? What is the
wavelength of the wave? Which type of wave is that?
(a) [2.5 x 1014 Hz]
(b) [1.2 x 10 -6]
(c) Infrared
Types of Waves
Transverse Waves
 Transverse Waves
Whenever the motion of the medium is at right
angles to the direction in which a wave travels
Longitudinal Waves
 Longitudinal Waves
Whenever the particles of the medium moves backand-forth along the direction of the wave rather than
at right angles to it
Combination of Waves
 Combination of Transverse & Longitudinal Waves
Water waves are an example of a combination of
both longitudinal and transverse motions. The
particles travel in clockwise circles
Longitudinal or Transverse?
Interference
Interference
 More than one vibration or wave can exist at the
same time in the same space
Interference
 The principle of
superposition of waves
states that the resultant
displacement at a point is
equal to the vector sum of
the displacements of
different waves at that
point
Constructive Interference
 The two waves are in-phase with each other they
add together
Constructive Interference
 The two waves are in-phase with each other they
add together
Destructive Interference
 The two waves are 180° out-of-phase with each
other they cancel
Destructive Interference
 The two waves are 180° out-of-phase with each
other they cancel
Interference Patterns
 Two waves overlap each other will form an
interference pattern
Interference Patterns
 Gray “spokes”:
zero amplitude
 Dark- & light-striped: crests of one wave overlap
the crests of another, and the troughs overlap as well
Reflection of Waves
 Reflection from a Fixed Boundary: at a fixed
boundary, the displacement remains zero and the
reflected wave changes its polarity
Reflection of Waves
 Reflection from an Open Boundary: at a free (soft)
boundary, the restoring force is zero and the
reflected wave has the same polarity as the incident
wave
Standing Waves
 A standing wave may be created from two travelling
waves with the same frequency (wavelength), the
same amplitude, and are travelling in opposite
directions in the same medium
Standing Waves
 The nodes are stable regions of destructive
interference and remain stationary
 The positions with the largest amplitudes are known
as antinodes. Antinodes occur halfway between
nodes
Standing Waves
 Various standing waves can be
produced by increasing the
frequency of vibrating string
Standing Waves
The wavelengths and frequencies of standing waves are:
Standing Waves
 The frequencies of the standing
waves on a particular string are
called resonant frequencies
 They are also referred to as the
fundamental and harmonics
Standing Waves
 Standing waves can be produced in either transverse
or longitudinal waves
 Various standing waves with open ended, close 1 end,
and close 2 ends
Doppler Effect
Doppler Effect
 The Doppler effect is the perceived change in
frequency of wave emitted by a source moving
relative to the observer
Doppler Effect
 When a wave source create ripple at a fixed position and
at constant frequency
 the crest of the wave are concentric circles
 the distance between wave crests (wavelength) will be the
same
 the wave speed is the same in all directions
 the frequency of wave motion at point A and B are the
same
A
B
Wavelength
Doppler Effect
 If the wave source moves across the water at a speed less
than the water speed, the wave motion at point A would
be at higher frequency than point B
 The greater speed of the source, the greater will be the
Doppler effect
 The Doppler effect is about the change of the perceived
frequency of the wave, not the change of wave speed
B
A
Short Wavelength
Doppler Effect Application
 Blue Shift: Light source approaches, frequency increases
 Red Shift: Light source recedes, frequency decreases
 A measurement of this shift enables astronomers to
calculate stars’ speeds of approaching or recession
Doppler Radar
Doppler Radar
Bow Waves & Shock Waves
Bow Waves
v=0
v < vw
Bow Waves
v=0
v = vw
v < vw
Bow Waves
v=0
v = vw
v < vw
v > vw
Bow Waves
v=0
v = vw
v < vw
v > vw
Bow Waves
v=0
v < vw
v = vw
v > vw
Bow Waves
 When the source moves the same speed of the waves,
the waves pile up and the overlapping wave crests
disrupt the flow of air
 When the source moves faster than the wave speed, the
overlapping crests create a V shape, called a bow wave
 The greater the moving speed produces a narrower V
shape
 An airplane can become supersonic and fly into smooth
and undisturbed air because no sound wave can
propagate out in front of it
Bow Waves
Shock Waves
 A speedboat generates a 2-D bow wave
 A supersonic aircraft generates a 3-D shock wave
 The conical shell of compressed air that sweeps behinds
a supersonic aircraft is called a sonic boom. The highpressure sound due to the overlapping crests has much
the same effect as an explosion
Shock Waves
Shock Waves
Shock Waves
The End