Music, Math, and Motion with Dr. Arun Chandra

1
Music, Math, and Motionwith Dr. Arun Chandra
Dr. E.J. ZitaThe Evergreen St. College

• Fall week 4
• Tuesday 21 Oct. 2008

2
Overview

• Looking ahead and resources (100-115)
• Acoustics and Instruments (half hour or so)
• Arun (half hour or so)
• 230-500 Watch Contact (150 minutes)
• Pick up your pink sheets on the way out just
  keep them in your portfolio with your lab
  worksheets

3
Looking ahead
Look at Moodle
http//elms.evergreen.edu/course/view.php?id27f4
4
Review resonant wavelengths

• How many waves fit in the length L of a guitar
  string?

5
Review resonant wavelengths

• How many waves fit in the length L of a guitar
  string?

Use that to find the resonant wavelengths ln
How are these related to the frequency and the
speed of oscillations of the guitar string?
v f l
6
Example from workshop Mandolin
DATA/OBSERVATIONS
? cm 35.7 26.7 17.85 23.8
f Hz 440 580 880 660
notes fundamental 1/4th length ½ length 1/3 length
speed
Ref Negative Nancy and the Newtrons, Workshop
2, week 3
7
Mandolin fundamental and harmonics
Graph of octave above A string
¼ above open A string
8
Speed of string oscillations
Speed of mandolin string oscillation ? speed of
sound in air (speed depends on physical
properties of medium) Frequency of mandolin
string oscillation f of tone heard in
air Predict will sound wavelength in air
resonant wavelength on guitar string?
? cm 35.7 26.7 17.85 23.8
f Hz 440 580 880 660
notes fundamental 1/4th length ½ length 1/3 length
Speed (m/s) 157 155 157 157
9
Resonant wavelengths for wind instruments Simple
approximations from last week
(e.g. flute)
(e.g. clarinet)
10
Clarinet tube closed on reed end
You might expect that
However, opening and closing combinations of
holes makes complex changes to resonant
wavelength
Johnston, Measured Tones (in Moodle
LecturesAndReadings)
11
More complex instruments
Stretched membranes (drums)
Rigden, Physics and the Sound of Music (in Moodle
LecturesAndReadings)
12
Speed and wavelength depend on medium
Frequency constant speed / wavelength Ex
Pluck open A string ? mandolin resonates _at_ 440 Hz
(157 m/s string oscillations) ? drives air
oscillations _at_ 440 Hz (with 330-340 m/s sound
speed in air speed, longer wavelength than
mandolins)