Waves: What are they

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Waves What are they?
Waves are used to describe things that are
periodic in nature (they repeat themselves)
Ocean Surface Wave
http//images.google.com/imgres?imgurlhttp//nees
.oregonstate.edu/killer_wave/wave.
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Physical phenomena that are wave-like.
Light, Heat, sound, X-Rays, radio waves,
microwaves, optics, heat radiation, . etc.
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Waves propagate two different ways

• Longitudinal
• Transverse

Compression in same direction as wave motion
slinky
the pressure wave travels back forth
Displacement is perpendicular to the wave motion
vibrating string
particles oscillate up down. Wave moves to right
Animation courtesy of Dr. Dan Russell, Kettering
University
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Wavelength, Frequency, Amplitude
Period is the time from crest to crest to pass as
the wave moves Frequency is the number of crest
that pass by each second
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How Waves are Produced

• Electromagnetic Waves
• Light, heat, X rays, Microwaves, radio waves, TV
  waves,
  
• .
• Mechanical Waves
• Sound waves, SONAR, seismic waves, ocean waves,
  .

Wave in a string
pulse
Pulse created by plucking the string. It travels
to the right.
Reflected pulse is inverted, then travels back.
reflected pulse
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Electromagnetic Waves
The wavelength of microwaves is about 10 cm while
the wavelength of an AM radio station is about
200 yards (183 m). Below is a graphical picture
of these two waves. It is not drawn to scale.
Visual comparison of microwaves radio waves
Not drawn to scale
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Mechanical Waves
Sound
When sound is created, air is compressed at the
source. This compression moves away from the
source with a velocity of around 1100 ft/s ( 330
m/s, which increases with temperature.
sound source
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How do waves combine?
Combine a sin(x) wave with a cos(2x) wave.
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Interference
When the wave sin(x) is combined with cos(2x),
they cancel each other where the arrows are. This
is called interference.
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How Noise Cancellation Headphones works
If the blue curve is received by the headphones,
then the phones electronically produce the red,
and the two add to zero (black line) everywhere.
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When lightning strikes, you can estimate the
distance
Estimate the speed of sound to be 1100 ft/s. Thus
in 5 s, sound would travel about 5500 ft, which
is roughly 1 mile.
So if you see lightning and start counting the
seconds to when you hear the thunder (1000, 1001,
1002,.), the distance 1 mile for every 5 s.
Suppose that you see lightning and immediately
begin counting 1000, 1001, 1002, and get to
1007, that means that the lightning is between 1
and 1 1/2 miles away. Remember that this is an
estimate.
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Physics Simulations
http//phet.colorado.edu/simulations/index.php?cat
Physics
Choose Sound Waves
Sound
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Standing Waves
If a string, tied on each end, is plucked on one
end, the pulse created moves from left to right.
Upon reflection, the wave inverts and moves to
the left. As the waves travels back forth, if
conditions are right, standing waves will be set
up. When this happens, the nodes (where the
string does not move up down) do not move from
left to right or vice versa.
http//www.answers.com/topic/standing-wave
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Frequencies of a String Instrument
If a string vibrates, and standing waves are
created, then the string can only vibrate with
certain frequencies (not all frequencies are
possible)
Below is a drawing of a string vibrating at its
lowest frequency (longest wavelength)
Fundamental Frequency
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Sounds From a String Instrument
Higher Frequencies
2nd Harmonic
3rd Harmonic
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Sounds From a String Instrument
5th Harmonic
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Sounds From a String Instrument
Guitar String Frequencies
E 82 Hz
A 110 Hz
D 147 Hz
G 196 Hz
B 247 Hz
E 660 Hz
E 660
C 523
A 440
F 350
www.guitarscores4u.com
C 261
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Frequencies of a String Instrument
Suppose that the A string is played and produces
f 110 Hz ( the fundamental frequency for that
string). While the string is vibrating, if we
lightly touch it at the center, what frequency do
we produce?
Length of string
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Frequencies of a String Instrument
Compare the frequency of the fundamental (110 Hz)
to that of the 3nd harmonic for a guitar string.
Length of string
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Frequencies of a Harmonica
A harmonica is sometimes called a free reed
instrument, because its sound is produced by
reeds which are fixed on one end (node) and free
on the other (antinode)
How is the sound of the Harmonica created?
It is not created by the vibration of the reeds.
It is created by the reed vibrating through the
slot and chopping the air stream. Reeds are not
like guitar strings, but more like springs that
interrupt the air stream past them.
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Free Reed Instruments
Concertina
accordion
free reed organ
Harmonica
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Free Reed Acoustics
modes
Reed
free end
L
fixed end
1st Harmonic
3rd Harmonic
2nd harmonic missing
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Free Reed Acoustics
Higher Harmonics
5th Harmonic
7th Harmonic
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Free Reed Acoustics
Harmonica Reed Frequencies
What is the length of a reed that has a
fundamental frequency 110 Hz?
Supposed that a harmonica reed length is measured
to be 0.5 cm, and the note generated is C 261 Hz.

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Free Reed Acoustics
Harmonica Reed Frequencies
Based on the previous calculation, determine the
length of a reed to produce 110 Hz.
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Tuning Fork
Pure (single frequency) wave
When we strike the fork gently with an object
(usually a wooden hammer) it begins to vibrate at
a specific frequency, usually written on the
fork. If the frequency is 440 Hz then the sound
that we hear is the note A 440.
This is a pure note with no other frequencies
contained in it.
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Why doesnt a flute sound like a clarinet if they
both play the same note?
Actually a better question would be why doesnt
any instrument sound like a tuning fork?
The answer is that a tuning fork produces a
single frequency while an instrument produces
several frequencies. The frequencies produced are
different for each instrument. This is sort of
like basic chili compared to your grandmothers
chili, which has several secret ingredients.
The different frequencies are called overtones.
If the note played is A 440 Hz, then the first
overtone is 880 Hz, and the one after that is 3 x
440 1320 Hz.
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Guitar spectral frequency for 220 Hz
Measured Frequency Spectrum for a Guitar
http//www.chandrakantha.com/articles/spectrum/spe
ctrum.html
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Guitar Waveform for 125 Hz
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Flute Waveform
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Guitar
Flute
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Why doesnt a flute sound like a clarinet if they
both play the same note?
Since these waveforms are very different, then
the sound produced by each is very different even
though they are playing the same note.
The same is true for each instrument, which give
s each one a distinct sound.
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Beats
Two notes of almost the same frequency produce
Beats.
Beat Frequency 4.77 - 3.98 0.79 Hz (1.26
s/Beat)
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Beats
Beats for two musical notes that are not quite
equal.
(0.2 Beats/s 5 s/Beat)
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Guitar Time Series
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Flute Time Series
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