lecture 15: sound waves - zhejiang...
TRANSCRIPT
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General Physics IGeneral Physics I
Lecture 15: Sound WavesLecture 15: Sound Waves
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OutlineOutline
● Sound frequency and sound level● Speed of sound waves● The physics of piano● The Doppler effect ● Shock waves
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Categories of Sound WavesCategories of Sound Waves
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Sound IntensitySound Intensity
● We define the intensity I of a wave, or the power per unit area, to be the rate at which the energy being transported by the wave flows through a unit area A perpendicular to the direction of travel of the wave.
amplitude
frequency
density
speed of sound
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Definition of Sound LevelDefinition of Sound Level
● Because the range of sound intensities is so wide, it is convenient to use a logarithmic scale, where the sound level is defined by the equation
● Threshold of pain:
(threshold of hearing)
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Sound LevelsSound Levels
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Speed of Sound in a SolidSpeed of Sound in a Solid
● If a solid bar is struck at one end with a hammer, a longitudinal pulse propagates down the bar with a speed
where Y is the Young’s modulus for the material and r the density of material.
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Elasticity in LengthElasticity in Length
● Young’s Modulus:
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The Speed of Sound Wave The Speed of Sound Wave
● In the continuous limit (in a solid),
∂2u
∂ t2= v2
∂2u
∂x2v=a√
KM
where
v
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Now, ...Now, ...
● Can you show that
are two equivalent forms of the speed of sound in the solid?
v = a√KM
(macroscopic) (microscopic)
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Speed of Sound in a FluidSpeed of Sound in a Fluid
● The speed of all mechanical waves follows an expression of the general form
We will, hopefully, come back to this issue in the part of thermodynamics for a complete understanding.
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Physics of the PianoPhysics of the Piano
Beauty is all about the frequency of the sound.
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Octave (8 Notes)Octave (8 Notes)
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Tone and PitchTone and Pitch
A pitch is a particular frequency of sound.
A musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre (or quality).
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Harmonic SpectrumHarmonic Spectrum
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Musical Scale (Pythagoras)Musical Scale (Pythagoras)
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Musical ScaleMusical Scale
● A4, fundamental frequency of 440 Hz• 21/12 = 1.05946… (equal temperament)• Perfect 5th, 27/12 = 1.4983…≈ 1.5
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What’s Inside?What’s Inside?
Physics in piano when making music.
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Vibrating Strings
f µ f (T,r,L)
Can you determine frequency by dimension analysis?
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Vibrating Strings
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Hammers that Hit the Strings
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Hammers that Hit the Strings
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Hammers That Hit the Strings
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Soundboard Producing Sound
Forced oscillations
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Soundboard Producing Sound2D
Generalization of the 1D cases
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Galilean Transformation Galilean Transformation
The two inertial observers agree on measurements of acceleration.
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Moving ObserverMoving Observer
We take the frequency of the source to be f, the wavelength to be l, and the speed of sound to be v.
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Analyze the Moving ObserverAnalyze the Moving Observer
● The speed of the waves relative to the observer is
● The wavelength l is unchanged.
Positive vO for observer moving toward source, and
negative vO for observer moving away from source.
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Moving SourceMoving Source
During each vibration, which lasts for a time T (the period), the source moves a distance
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Analyze Moving SourceAnalyze Moving Source
● For observer A, the wavelength is shortened to
● The frequency heard by observer A is
● For observer B, simply use a negative vS.
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Doppler EffectDoppler Effect
● Finally, if both source and observer are in motion, we find the following general relationship for the observed frequency:
f ' =v+vOv−vS
f
The word toward is associated with an increase in observed frequency. The words away from are associated with a decrease in observed frequency.
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Spherical WavesSpherical Waves
● The wave intensity at a distance r from the source is
● The intensity is proportional to the square of the amplitude. Hence,
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Echocardiogram (ECG)Echocardiogram (ECG)
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Shock WavesShock Waves
Mach number: vs / v
(vS > v )