RESONANCE

MUSICAL ACOUSTICS

Science of SoundChapter 4

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.

PHASE DIFFERENCE BETWEEN CRANK AND MASS

STANDING WAVES ON A STRING

OPEN AND CLOSED PIPES

OPENPIPE

CLOSEDPIPE

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

GRAPHING ACOUSTIC IMPEDANCE

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-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

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

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

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).