Waves
Overview
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Waves – What are they?
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Imagine dropping a stone into a still pond and
watching the result.
A wave is a disturbance that transfers energy
from one point to another in wave fronts.
•
Examples
• Ocean wave
• Sound wave
• Light wave
• Radio wave
Waves – Basic Characteristics
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Frequency (f)
cycles/sec (Hz)
Period (T)
seconds
Speed (v)
meters/sec
Amplitude (A)
meters
Wavelength ( )
meters
Peak/Trough
Wave spd = w/length * freq
•
v=
*f
Wave – Basic Structure
Wave Types
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2 types of waves:
• Electromagnetic
• Require NO medium for transport
• Speed is speed of light @ 3 x 108 m/s
• Examples – light, radio, heat, gamma
• Mechanical
• Require a medium for transport of energy
• Speed depends on medium material
• Examples – sound, water, seismic
Waves – Electromagnetic
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Wave speed is 3 x 108 m/s
Electric & Magnetic fields are perpendicular
Waves – Radio
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Electromagnetic type
Most radio waves are broadcast on 2
bands
• AM – amplitude modulation (550-1600 kHz)
• Ex. WTON 1240 kHz
• FM – frequency modulation (86 – 108 MHz)
• Ex. WMRA 90.7 MHz
• What are their respective wavelengths?
Practice
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What is the wavelength of the radio
carrier signal being transmitted by
WTON @1240 kHz?
Solve c = λ*f for λ.
• 3e8 = λ * 1240e3
• λ = 3e8/1240e3 = 241.9 m
Practice
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What is the wavelength of the radio
carrier signal being transmitted by
WMRA @ 90.7 MHz?
Solve c = λ*f for λ.
• 3e8 = λ * 90.7e6
• λ = 3e8/90.8e6 = 3.3 m
Mechanical Waves
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2 types of mechanical waves
• Transverse
• “across”
• Longitudinal
• “along”
Waves – Mechanical Transverse
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Transverse
•
Particles move perpendicularly to the wave motion
being displaced from a rest position
• Example – stringed instruments, surface of liquids
>> Direction of wave motion >>
Waves - Mechanical
Longitudinal
• Particles move parallel to the wave motion,
causing points of compression and rarefaction
• Example - sound
>> Direction of wave motion >>
Longitudinal Waves
Sound
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Speed of sound in air depends on temperature
• Ss = 331 + 0.6(T) above 0˚C
• Ex. What is the speed of sound at 20 C?
• Ss = 331 + 0.6 x 20 = 343 m/s
Speed of sound also depends upon the
medium’s density & elasticity. In materials with
high elasticity (ex. steel 5130 m/s) the
molecules respond quickly to each other’s
motions, transmitting energy with little loss.
• Other examples – water (1500), lead (1320)
hydrogen (1290)
Speed of sound = 340 m/s (unless other info is given)
Sounds and humans
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Average human ear can detect &
process tones from
• 20 Hz (bass – low frequencies) to
• 20,000 Hz (treble – high frequencies)
Doppler Effect
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What is it?
• The apparent change in frequency of sound due
to the motion of the source and/or the observer.
Doppler Effect
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Moving car example
Doppler Effect Example
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Police radar
Doppler Effect Formula
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f’ = apparent freq
f = actual freq
v = speed of sound
vo = speed of observer
(+/- if observer moves
to/away from source)
vs = speed of source
(+/- if source moves
to/away from the
observer)
Video example
v vo
f' f
v vs
Sound Barrier #1
Sound Barrier #2
Doppler Practice
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A police car drives at 30 m/s toward the
scene of a crime, with its siren blaring at a
frequency of 2000 Hz.
• At what frequency do people hear the siren as
•
it approaches?
At what frequency do they hear it as it passes?
(The speed of sound in the air is 340 m/s.)
Doppler Practice
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A car moving at 20 m/s with its horn
blowing (f = 1200 Hz) is chasing another
car going 15 m/s.
• What is the apparent frequency of the horn as
heard by the driver being chased?
Interference of Waves
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2 waves traveling in
opposite directions in the
same medium interfere.
Interference can be:
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Constructive (waves
reinforce – amplitudes add
in resulting wave)
Destructive (waves cancel
– amplitudes subtract in
resulting wave)
Termed - Superposition
of Waves
Superposition of Waves
Superposition of Waves
Special conditions for amp, freq and λ…
Standing Wave?
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A wave that results from the interference of 2 waves
with the same frequency, wavelength and amplitude,
traveling in the opposite direction along a medium.
There are alternate regions of destructive (node) and
constructive (antinode) interference.
Standing Wave
2 models for discussion…
Standing Waves in Strings
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Nodes occur at each
end of the string
Harmonic # = # of
envelopes
fn = nv/2L
•
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f = frequency
n = harmonic #
v = wave velocity
L = length of string
Standing Waves in Strings
Practice
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An orchestra tunes up by playing an A
with fundamental frequency of 440 Hz.
• What are the second and third harmonics of
this note?
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Solve fn = n*f1
• f1 = 440
• f2 = 2 * 440 = 880 Hz
Practice
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A C note is struck on a guitar string,
vibrating with a frequency of 261 Hz,
causing the wave to travel down the string
with a speed of 400 m/s.
• What is the length of the guitar string?
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Solve f = nv/(2L) for L
• L = nv/(2f)
• L = 0.766 m
Standing Waves in Open Pipes
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Waves occur with
antinodes at each end
fn = nv/2L
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•
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f = frequency
n = harmonic #
v = wave speed
L = length of open pipe
Standing Waves in Pipes (closed
at one end)
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Waves occur with a
node at the closed end
and an antinode at the
open end
Only odd harmonics
occur
fn = nv/4L
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•
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f = frequency
n = harmonic #
L = length of pipe
Practice
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What are the first 3 harmonics in a 2.45
m long pipe that is:
• Open at both ends
• Closed at one end
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Solve
• (open) fn = nv/(2L)
• (closed @ 1 end) fn = nv/(4L)
Beats
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Beats occur when 2 close frequencies (f1, f2)
interfere
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Reinforcement vs cancellation
Pulsating tone is heard
Frequency of this tone is the beat frequency (fb)
fb = |f1 - f2|
Beats
f1
f2
|f1-f2|