resonance musical acoustics science of sound chapter 4
TRANSCRIPT
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RESONANCE
MUSICAL ACOUSTICS
Science of SoundChapter 4
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ResonanceResonance occurs when a vibrating system is driven at its natural frequency.
The amplitude of the vibrator reaches a maximum, limited only by the damping.
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PHASE DIFFERENCE BETWEEN CRANK AND MASS
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STANDING WAVES ON A STRING
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OPEN AND CLOSED PIPES
OPENPIPE
CLOSEDPIPE
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STANDING WAVES IN
CYLINDRICAL AND CONICAL
PIPES
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ACOUSTIC IMPEDANCE
Acoustic impedance is the ratio of sound pressure p to volume velocity U
ZA = p/U
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GRAPHING ACOUSTIC IMPEDANCE
APPARATUS FOR GRAPHING THE ACOUSTIC IMPEDANCE OF WIND INSTRUMENTS
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HELMHOLTZ RESONATOR
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HELMHOLTZ RESONATOR
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TUNING FORK
D.A. Russell, "On the sound field radiated by a tuning fork," Am. J. Phys., 68(12), 1139-45 (2000).
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CHOIRCHIMES
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CHOIRCHIME VIBRATIONS
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SINGING RODS AND WINEGLASSES
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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
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SELF-EXCITATIONA 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
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SELF-EXCITATIONA 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
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COLLAPSE OF THE TACOMA NARROWS BRIDGE
A DRAMATIC CASE OF SELF-EXCITED OSCILLATION
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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.
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Assignment for January 21
Read Chapter 5Exercises 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).