The Physics of Music - Physics 15 University of California, Irvine ...

The Physics of Music - Physics 15
University of California, Irvine
Instructor: David Kirkby
dkirkby@uci.edu
Air Columns as Resonators
The air contained within a pipe can resonate just like a
string. What are the corresponding boundary conditions
Nodes and Anti-Nodes in an Air Column
(1) fixed + free ends
(2) two free ends
(3) two fixed ends
……open + closed ends
……two open ends
……two closed ends (!)
Listen to the heated “hoot tube” demonstration for an
example of resonance in a tube open at both ends.
Physics of Music, Lecture 5, D. Kirkby 31
Physics of Music, Lecture 5, D. Kirkby 32
Demonstration: Singing Rod
A long aluminum rod can sustain two kinds of vibrations:
• Longitudinal (squeezing & stretching along its length)
• Transverse (bending transverse to its length)
Complex Driving Forces
The demonstrations of singing rods, plucked strings and
hoot tubes that you heard today appear to be missing one
of the crucial ingredients for resonance:
That energy is provided periodically at a
constant driving frequency.
Since these two resonances involve fundamentally different
types of motion, their fundamental frequencies have no
simple relationship.
We were able to excite resonances in all three cases
without paying attention to the frequency at which
energy was provided. Why
Watch and listen to the vibrations of an aluminum rod.
What were the boundary conditions
Physics of Music, Lecture 5, D. Kirkby 33
Physics of Music, Lecture 5, D. Kirkby 34
Noisy Energy Sources
Plucking a string, heating the air near a metal mesh, and
drawing your fingers along a rod are all examples of noisy
energy sources.
Noise is the superposition of many simultaneous
vibrations (of air, a string, a rod, …) covering a
continuous range of frequencies.
Since no single frequency dominates, we do not hear a
definite pitch, even though all frequencies are present!
Since all frequencies are present in some range, we are
guaranteed to excite any resonances present within the
range.
Summary
Resonance is a buildup of energy when it is delivered at
the right frequency.
Many physical systems are resonant. Some have more than
one kind of resonant response (eg, the singing rod).
A system may have several resonant frequencies for the
same type of response.
Examples of resonance: swing, rope fixed at both end, air
column, aluminum rod.
Physics of Music, Lecture 5, D. Kirkby 35
Physics of Music, Lecture 5, D. Kirkby 36
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