??? Mechanical Waves

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??? Mechanical Waves

• Mechanical wave is a disturbance that travels
  through some material or substance called the
  medium for wave.
• Transverse wave is the wave that the displacement
  of the medium are perpendicular or transverse to
  the direction of travel of the wave along the
  medium
• Longitudinal wave is the wave that the motions of
  particles is the same as the direction of wave.

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??????(Dimensional Analysis) ???????????????????m
??????t
????? ????
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Mathematical Description of a Wave
sinusoidal wave moving in x-direction
Phase
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Energy in Wave Motion
The instantaneous rate of doing work at the point
x and time t is
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Maximum Power
average power, sinusoidal wave on a string
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Average intensity
inverse-square law for intensity
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Wave Interference Boundary Conditions and
Superposition
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Overlap of two wave pulses
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standing wave on a string, fixed end at x 0
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Normal Modes of a String
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?????(Fourier Analysis)
f(t)??????
????(fundamental frequency)T?f(t)????
????
??????????,???????(harmonics)
n????
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?f(t)?t????
?f(t)?t????
?? ??????????(sawtooth wave)
??????(1)n3 (2)n7???
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Sound Waves
Sound is a longitudinal wave in a medium Audible
range of human ear is 20 to 20000Hz
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Gauge pressure
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Gauge pressure
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In a sinusoidal sound wave the max pressure
variations are 3.010-2Pa above the atmospheric
pressure. Find the max displacement if frequency
is 1000Hz. Given speed of sound is 344m/s and
bulk modulus is 1.42105Pa
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The Anatomy of Human Ear
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Sound Velocity and Gauge Pressure
intensity of a sinusoidal sound wave
definition of sound intensity level
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???bulk modulus
??????,pVnRT,
???????????????????????,????,????????????,???????,
?
?
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He?STP,M04.00 kg/kmole, g5/3
???He??,???????,????
??0????
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Beats ??
??????????????????????lt7Hz
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16.8 The Doppler effect
Moving listener and stationary source
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Moving source and moving listener
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People used Doppler flow meter to measure the
blood flow rates. The speed of sound in blood is
known to be 1570 m/s and a typical red blood cell
has a radius of 5µm. Please estimate what would
be the frequency for the flow meter?
If the frequency shift measured by the Doppler
flow meter is 100Hz (the meter was operated at
107Hz), please find the average velocity of blood
flow.
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Shack Wave (Sonic Boom)
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??(transverse wave)?????????????(shear strain)
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??(longitudinal wave)??????????????(tensile
strain)????????(tensile stress)
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(a)?????7.83103 kg/m3,G8.31010 Pa,???????????
(b)?????????12800 m/s,???3.51103 kg/m3,??shear
modulus?