# RESONANCE CHAPTER 4

MUSICAL ACOUSTICS
RESONANCE
Science of Sound
Chapter 4
Resonance
Resonance occurs when a vibrating system is driven at
its natural frequency.
The amplitude of the vibrator reaches a maximum,
limited only by the damping.
PHASE DIFFERENCE BETWEEN CRANK AND MASS
STANDING WAVES ON A STRING
OPEN AND CLOSED PIPES
OPEN
PIPE
CLOSED
PIPE
STANDING
WAVES IN
CYLINDRICAL
AND
CONICAL
PIPES
ACOUSTIC IMPEDANCE
Acoustic impedance is the ratio of sound
pressure p to volume velocity U
ZA = p/U
APPARATUS FOR
GRAPHING THE
ACOUSTIC
IMPEDANCE OF
WIND
INSTRUMENTS
HELMHOLTZ RESONATOR
HELMHOLTZ RESONATOR
TUNING FORK
D.A. Russell, "On the sound field radiated by a tuning fork," Am. J.
Phys., 68(12), 1139-45 (2000).
CHOIRCHIMES
CHOIRCHIME VIBRATIONS
SINGING RODS AND WINEGLASSES
SINGING RODS
In a bar or rod with free ends the
fundamental mode will have a
node at its center, and the
maximum vibration occurs at the
ends (just as in a pipe open at
both ends).
The next mode has two modes at
¼ L and ¾ L
Stroking an aluminum rod with the
fingers to excite these longitudinal
resonances can create rather loud
sounds
SELF-EXCITATION
A linear force or motion can excite vibratory motion by
a process called self-excitation.
Examples of this are the
stick-slip motion that excites
a wineglass or a violin string
SELF-EXCITATION
A linear force or motion can excite vibratory motion by
a process called self-excitation.
Examples of this are the
stick-slip motion that excites
a wineglass or a violin string
COLLAPSE OF THE TACOMA NARROWS BRIDGE
A DRAMATIC CASE OF SELF-EXCITED OSCILLATION
SYMPATHETIC VIBRATION
The vibrating string of a piano or guitar excites the
soundboard to vibrate (and thus to produce much
more sound). This is called sympathetic vibration.
Sympathetic vibration and self-excitation of vibration
should not be confused with resonance.
Assignment for January 21
Exercises 1-8 (p.73)
For extra credit:
Driven harmonic analyzer (“Texas tower”)
Make a graphs of amplitude vs frequency and
phase angle vs frequency for 2 amounts of damping
Show the modes of a wineglass that can be excited by
rubbing with a finger; bowing radially with a violin
bow; driving it with a loudspeaker.
Ref: J. Acoust. Soc. Am. 95, 1108-1111 (1994).

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