```Grade 11 Physics
Waves
The Nature of Waves
1. A wave is a travelling disturbance
2. A wave carries energy from place to place
Wave Pulse
• A single disturbance that travels through a
medium
• A wave of short duration
Periodic Waves
• If the disturbance repeats itself regularly then
a periodic wave is generated.
Note
• It is the disturbance that travels through the
medium, not the medium itself.
Important
• Regardless of the nature of the wave (sound, slinky,
water, etc) or the medium through which it travels
(air, solid, liquid, etc.) all waves exhibit wave-like
behaviour (interference, diffraction, refraction, etc.)
and can be described using the same terminology
(amplitude, wavelength, speed, etc.) and the same
mathematical equations
• When I use sound waves to demonstrate and
illustrate the Doppler effect for example, it is not
because only sound waves exhibit this effect. In fact
all waves exhibit this effect. It’s just easiest to
demonstrate it with sound waves.
Here is the first exception …
• Two basic types of waves:
• If the disturbance is
perpendicular to the direction
of propagation of the wave it is
called a transverse wave
• If the disturbance is parallel to
the direction of propagation of
the wave it is called a
longitudinal wave
crest
trough
Periodicity
• Examples: pendulum, rocking chair, engine
cycle, Earth’s orbit, etc.
• When talking about anything that repeats
itself at regular time intervals we can define …
• The Period T: The time for one complete cycle
• The frequency f: The number of complete
cycles per unit time
• What is the relationship between these two?
Example: Earth’s rotation
Period
Time Unit
Frequency
24
hours
1/24
1
days
1
1/7
weeks
7
1/365
years
365
• Period and frequency are reciprocals
1
T
f
1
f 
T
Assignment
Speed of a wave
• The speed of a wave depends on the physical
properties of the medium
• Examples:
– Waves travel faster through stiffer springs
– Speed of waves in water depends on the depth
– Sound waves travel faster in warmer air
Reflection
• Fixed-end
• Free end
Reflection and Transmission
• Occurs at the
boundary where
the speed of wave
changes
Interference
• What happens when two waves meet?
• Wave interference occurs when two waves act
simultaneously on the same particles of a medium.
There are two types of interference: constructive and
destructive.
• destructive interference occurs when a crest meets a
trough resulting in a lower amplitude
• Constructive interference occurs when pulses build
each other up, resulting in a larger amplitude (crest
meets a crest or trough meets a trough)
The Nature of Sound
• Longitudinal wave that is created by a
vibrating object
• Sound wave consists of traveling pulses of
high pressure zones, or condensations,
alternating with travelling pulses of low
pressure zones, or rarefactions
• These pressure fluctuations are normally very
small
• Sound requires a medium (gas, liquid, or solid)
• Cannot exist in a vacuum
The frequency of a sound wave
• A sound with a single frequency is called a pure tone
• Human hearing
–
–
–
–
–
You can hear sounds from 20 Hz to 20000 Hz (20 kHz)
Me…up to about 12 -14 kHz
Infrasonic (<20 Hz) Ultrasonic (>20 kHz)
Rhinos use infrasonic (down to 5 Hz)
Bats use ultrasonic (up to 100 kHz)
• The brain interprets the frequency detected by the ear
in terms of pitch
• High pitch corresponds
to high frequency
• Low pitch corresponds
to low frequency
The Speed of Sound
• Sound travels through gases, liquids, and
solids, at considerably different speeds
• At room temp in air its approx 343 m/s
• Moves 4 times faster in water
• Moves 17 times faster in solids
• Speed increases with temp
– Air (0°C) 331 m/s
– Air (20°C) 343 m/s
• Unless otherwise stated
assume air at 20°C
Natural Frequency
• Nearly all objects when hit, struck, plucked, or
strummed will vibrate
• They tend to vibrate at a particular frequency
(or set of frequencies) called the natural
frequency
• Some tend to vibrate at a single frequency
(pure tone) like a flute or a tuning fork while
others vibrate at a set of frequencies
• The natural frequency of an object is
determined by its physical properties
• Example: Guitar String
– Linear density
– Tension
– Length
Flute
• 200 Hz
Tuba
• 200 Hz
• 400 Hz
• 600 Hz
• 800 Hz
• 1000 Hz
Dropped Pencil
• 197 Hz
• 211 Hz
• 217 Hz
• 219 Hz
• 287 Hz
• 311 Hz
• 329 Hz
• 399 Hz
Forced Vibration
• The tendency of one vibrating object to force
another object into vibrational motion
• A louder sound is always produced when an
accompanying object of greater surface area is
forced into vibration
• Examples
– Wooden body of a guitar
– Sounding board in a piano
Resonance
• Occurs when the frequency of forced vibration
matches the natural frequency of the second
object
• The result is always a large vibration
Interference
• Sound waves, like any waves, can be made to
exhibit interference
• When two or more sound waves from
different sources are present at the same
time, they interact with each other to produce
a new wave.
• The new wave is the sum of all the different
waves.
• Wave interaction is called interference.
• If the compressions and the rarefactions of
the two waves line up, they strengthen each
other and create a wave with a higher
intensity.
• This type of interference is known as
constructive.
• When the compressions and rarefactions are
out of phase, their interaction creates a wave
with a dampened or lower intensity.
• This is destructive interference.
Beats
• A special case of interference occurs when
two tones of slightly different frequencies are
sounded together
• A fluctuation in the loudness, called beats, is
heard
• The frequency of the beats is equal to the
difference in frequencies
• Example: If a 262 Hz and 266 Hz tuning forks
are sounded together the beat frequency will
be …
• … 4 Hz !!!!
Diffraction
• the bending of waves around obstacles and
the spreading out of waves beyond openings.
• Most pronounced when the wavelength is
comparable to the size of the opening or
obstacle
Doppler Effect
• is the change in frequency of a wave for an
observer moving relative to the source of the
wave.
• It is commonly heard when a vehicle sounding
a siren or horn approaches, passes, and
recedes from an observer.
• The received frequency is higher (compared to
the emitted frequency) during the approach, it
is identical at the instant of passing by, and it
is lower during the recession.
Doppler effect
What is light?
• Particle or wave?
• Up until 1801 there were two competing
theories –light as a wave and light as a particle
• Both theories could explain the then known
properties of light, namely reflection and
refraction
Young’s Double Slit Experiment
(1801)
• Showed that light was a wave
James Clerk Maxwell
• In 1865 he proposed the existence of electromagnetic waves
produced by the vibration of electric charges
• When he calculated the speed at which such waves should
propagate it came out to a value very close to that of the speed
of light
• He concluded that light was a form of electromagnetic radiation
Electromagnetic Spectrum
But then …
• Albert Einstein (1905) explained the photoelectric effect by
theorizing that light is composed of particles whose energy
depended on the frequency of the light
• He called these particles photons
Wave-particle duality
linear wave equations, but can only be emitted or
absorbed as discrete elements, thus acting as a wave
and a particle simultaneously.
• In 1924, Louis-Victor de Broglie formulated the de
Broglie hypothesis, claiming that all matter, not just
light, has a wave-like nature
• This was confirmed 3 years later when electrons
were observed to behave like waves and form
interference patterns
The Speed of Light
• Ole Romer first demonstrated in 1676 that light
travelled at a finite speed (as opposed to
instantaneously)
• First accurate measurement was made in 1880 by
Albert Michelson
• The speed of light in vacuum, usually denoted by
c, is a physical constant important in many areas of
physics. Its value is 299,792,458 metres per
second
8
c  3.0 10 m / s
Refraction
• Refraction is the
change in
direction of a
wave due to a
change in its
speed.
Index of refraction
c
n
v
Snells Law
Laser Light
• Light emitted by a common lamp has many
different frequencies and it tends to spread
out after a short distance becoming wider and
wider and less intense with increased distance
• It is said to be incoherent
• A beam of light that has the same frequency
and direction is said to be coherent
• Coherent light is produced by a laser
Example
• A laser emits a coherent light beam with a wavelength
of 650 nm. What is the frequency of the wave?
n=4 fourth order
n=3 third order
n=2 second order
n=1 first order
n=o central bright
n=1 first order
n=2 second order
n=3 third order
n=4 fourth order
• http://www.acoustics.salford.ac.uk/feschools/
index.htm
• http://www.acoustics.salford.ac.uk/feschools/
waves/flash/huygens.swf
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