MUSICAL ACOUSTICS Chapter 2 VIBRATING SYSTEMS. SIMPLE HARMONIC MOTION A simple vibrator consisting...
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Transcript of MUSICAL ACOUSTICS Chapter 2 VIBRATING SYSTEMS. SIMPLE HARMONIC MOTION A simple vibrator consisting...
![Page 1: MUSICAL ACOUSTICS Chapter 2 VIBRATING SYSTEMS. SIMPLE HARMONIC MOTION A simple vibrator consisting of a mass and a spring. At equilibrium (center), the.](https://reader035.fdocuments.net/reader035/viewer/2022062320/56649d585503460f94a37ba2/html5/thumbnails/1.jpg)
MUSICAL ACOUSTICSMUSICAL ACOUSTICS
Chapter 2
VIBRATING SYSTEMSVIBRATING SYSTEMS
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SIMPLE HARMONIC
MOTION
A simple vibrator consisting of a mass and a spring. At equilibrium (center), the upward force exerted by the spring and the force of gravity balance each other, and the net force F on the mass is zero.
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Simple Harmonic Motion
Graphs of simple harmonic motion:
(a) Displacement versus time(b) Speed versusTime. Note that speed reaches itsmaximum whendisplacement is zero and vice versa.
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Vibratory motion: y,v, and a all change with time.
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Displacement of a damped vibrator whose amplitude decreases with time
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EVERY VIBRATING SYSTEM HASInertia (mass)Elasticity (spring)
For a mass/springHooke’s LawF = Ky
In Chapter 1 we learned that KE= ½ mv2
Similarly, it can be shown that PE = ½ Ky2
If the vibrator has damping:
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A mass hangs from a spring. You raise the mass 1 cm, hold it there for a short time and then let it drop
Make a graph of its motion
Make a graph of its total energy.
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SIMPLE VIBRATING SYSTEMS
A simplependulum
ƒaƒƒƒƒƒ
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A mass-spring system vibrates at a frequency f If the mass is doubled:a) The frequency will be 2fb) The frequency will be √2fc) The frequency will remain fd) The frequency will be f/√2e) The frequency will be f/2
A mass swings on the end of a string at frequency f
If the mass is doubled:a) The frequency will be 2fb) The frequency will be √2fc)The frequency will remain fd) The frequency will be f/√2e) The frequency will be f/2
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SIMPLE VIBRATING SYSTEMS
A piston free tovibrate in a Cylinder
A Helmholtz Resonator
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SYSTEMS WITH TWO MASSES
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Longitudinal vibrations of a three-mass vibrator
Transverse vibration of a three-mass vibrator
Transverse vibrations for spring systems with multiple masses
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LINEAR ARRAY OF OSCILLATORS
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MODES OF CIRCULAR MEMBRANES
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BASS DRUM
SNARE DRUM
TIMPANI
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VIBRATING BARS
Both ends free One end clamped
Arrows locate the nodes
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CHLADNI PATTERNS OF A CIRCULAR PLATE
SaltS
SALT COLLECTS AT THE NODES
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VIBRATIONAL MODES OF A CYMBAL (top)
AND A CIRCULAR
PLATE (bottom)
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CYMBALS GONG TAM TAM
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VIBRATIONS OF A TUNING FORK