Wave

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Wave
Longitudinal Wave
Transverse Wave
Difference between transverse and longitudinal
wave
TransverseThe motion is perpendicular to the
waves direction of travel Longitudinal The
motion is parallel to the waves direction of
travel
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Period, Frequency, Wavelength and Amplitude
T Period (unit second)
When motion repeats itself for each time
interval, this time interval is period
f frequency (unit Hertz, Hz)
Number of oscillations per second
v speed of wave(unit m/s)
? Wavelength(unit m)
Traveling distance of wave during one period
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Period, Frequency, Wavelength and Amplitude
ym Period (unit meter, cm, mm...)
Maximum displacement of wave
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T 1s
I. What is the period of this wave?
II. What is the frequency of this wave?
III. What is the amplitude of this wave?
IV. If the speed of this wave is 344 m/s, what
is its wavelength?
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Constructive Interference
y
t
In phase
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Destructive Interference
y
t
Out of phase
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Beats

• Pure tone a sound wave with a single frequency
• When two pure tones have slightly different
  frequencies, we hear average frequency and the
  difference frequency.
• Difference frequency Beats

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Situation

• You wish to tune the note A3 on a piano to its
  proper frequency of 220 Hz. You have available a
  tuning fork whose frequency is 440 Hz. How
  should you proceed?

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Standing Wave
When two waves of the same amplitude and
wavelength travel in opposite directions along a
stretched string, their interference with each
other produces a standing wave.
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How are standing waves formed????
Generation of many overlapping waves due to
reflection
Interference between waves
Standing wave can be formed
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For even instruments with open ends (organs, the
standing waves are formed.
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antinode
node
Node place where the amplitude of the standing
wave is zero
Antinode place where the amplitude of the
standing wave is maximum
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When an end is fixed, nodes will be formed. When
an end is open, antinodes will be formed.
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Resonance
When a string or an air column is vibrated with
one of its fundamental frequency, it will produce
the standing wave.
Resonance Resonance frequency
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Advantage of Standing Wave
For a guitarist,
String oscillates with a large, sustained
amplitude, pushing back and forth against the
surrounding air, and thus generating a noticeable
sound wave with the same frequency as the
oscillations of the string.
For an organist,
Air column oscillates with a large, sustained
amplitude, pushing back and forth against the
surrounding air, and thus emitting at any open
end a sound wave that has the same frequency as
the oscillations of the string.
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Guitar Both End Fixed
In general, resonant frequencies of standing
wave,
, n1,2,3,.
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Guitar Both End Fixed
Resonant frequencies of standing wave,
, n1,2,3,.
When n1, the lowest resonant frequency
Fundamental mode First harmonic
When n2, the lowest resonant frequency
Second harmonic
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Harmonics
Whole number multiples of the fundamental mode
n Harmonic number
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Instruments with Both Open Ends
, n1,2,3,.
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Instrument with One Open End
, n1,3,5,. Odd numbers
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Instrument with One Open End
, n1,3,5,. Odd numbers
Even harmonics are MISSING!!!!!
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First or higher harmonics are generated
simultaneously in any musical instrument.
Sound we hear combination of all harmonics
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Partials , Overtones, and Vibration Spectrum
Overtones higher modes of vibration Second
harmonics first overtone Third
harmonics second overtone Partial A mode of
vibration including the fundamental mode plus
overtones Vibration Spectrum A recipe that
specifies the relative amplitudes of the
partials
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Vibrations and Sounds
The amount of sound radiated by a vibrating
system depends on the amount of air it displaces
as it moves
Ex) Vibrating string or the narrow prongs of the
tuning fork small amount of sound
Loudspeaker or drums
Large area to vibrate
Large displacement of air
Loud sound
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Sympathetic Vibrations Soundboards
Tuning fork mounted on a wooden box
Violin, guitars, cellos, and other string
instruments depends strongly on sympathetic
vibration of the wood box
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Tuning Fork

• Frequency of tuning fork remains fundamental
  frequency for a long time once adjusted.
• Frequency of tuning fork can be changed by the
  change of its length and by the change of its mass