Music, Math, and Motion with Dr. Arun Chandra

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Music, Math, and Motionwith Dr. Arun Chandra
Dr. E.J. ZitaThe Evergreen St. College

• Fall week 2
• Tuesday 7 Oct. 2008

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Overview

• Review Simple Harmonic Motion (SHM)
• Kinematics
• Tension ? Speed of waves
• Force ? Power ? Intensity
• Perception of sound

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Simple Harmonic Motion (SHM)

• Loy p.130

s
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Simple Harmonic Motion sine wave
s
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Example of SHM Jupiters moons
s
http//www.pacifier.com/tpope/Galilean_Moons_of_J
upiter_2PB280064.jpg
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Doubting the celestial crystal spheres
http//ircamera.as.arizona.edu/NatSci102/NatSci102
/lectures/copernicus.htm
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Four lesser stars near Jupiter moved(Brecht
p.208)
http//edu.kde.org/kstars/feature/JMoonTool.png
http//www.hao.ucar.edu/Public/education/bios/gali
leo.4.html
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Positions of Jupiters moons ? time ? longitude!
http//www.skyandtelescope.com/observing/objects/j
avascript/3307071.html?page2cy
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Observe moons of Jupiter ? tell time ? determine
longitude (p.217)
As these new astronomical charts enable us to
determine longitudes at sea and so make it
possible to reach the new continents by the
shortest routes, we would beseech Your Excellency
to aid us in reaching Mr. Galilei, mathematician
to the Court of Florence, who is now in
Rome --- From a letter written by a member of
the Genoa Chamber of Commerce and Navigation to
the Papal Legation.
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Example of SHM Acoustic waves
s
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Kinematics
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Tension ? Speed of waves
Tension is a force, with units of Newtons Guess
what the speed of waves on a plucked guitar
string depends on?
Guess what the speed of acoustic waves in air
depends on?
Now consider plucking a magnetic field line.
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Force ? Energy ? Power
Mechanical energy Work Force
displacement Mechanical energy Kinetic Energy
Potential Energy Kinetic Energy ½ mv2 Potential
energy ability to do work
Units of Energy Force (N) Displacement (m)
Joules Nm
Power rate of doing work Energy / time
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Force ? Pressure? Intensity
Pressure Force / Area Intensity Power / Area
rate of energy flow / across a surface
area (typo in Loy (4.34) p.118)
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Perception of sound
Doubling the intensity of sound does not double
our perception of loudness. The human ear
perceives sound intensity nonlinearly. To
produce a sound that seems twice as loud requires
a sound wave that has about then times the
intensity. (Giancoli, Physics for scientists and
Engineers, p.420)
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Perception of sound