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...
MUSICAL ACOUSTICSMUSICAL ACOUSTICS
Chapter 2
VIBRATING SYSTEMSVIBRATING SYSTEMS
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.
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.
Vibratory motion: y,v, and a all change with time.
Displacement of a damped vibrator whose amplitude decreases with time
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:
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.
SIMPLE VIBRATING SYSTEMS
A simplependulum
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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
SIMPLE VIBRATING SYSTEMS
A piston free tovibrate in a Cylinder
A Helmholtz Resonator
SYSTEMS WITH TWO MASSES
Longitudinal vibrations of a three-mass vibrator
Transverse vibration of a three-mass vibrator
Transverse vibrations for spring systems with multiple masses
LINEAR ARRAY OF OSCILLATORS
MODES OF CIRCULAR MEMBRANES
BASS DRUM
SNARE DRUM
TIMPANI
VIBRATING BARS
Both ends free One end clamped
Arrows locate the nodes
CHLADNI PATTERNS OF A CIRCULAR PLATE
SaltS
SALT COLLECTS AT THE NODES
VIBRATIONAL MODES OF A CYMBAL (top)
AND A CIRCULAR
PLATE (bottom)
CYMBALS GONG TAM TAM
VIBRATIONS OF A TUNING FORK