Music, Math, and Motion with Dr. Arun Chandra & Dr. E.J. Zita The Evergreen St. College Fall week 4 Tuesday 21 Oct. 2008.

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Presentation transcript:

Music, Math, and Motion with Dr. Arun Chandra & Dr. E.J. Zita The Evergreen St. College Fall week 4 Tuesday 21 Oct. 2008

Overview Looking ahead and resources (1:00-1:15) Acoustics and Instruments (half hour or so) Arun (half hour or so) 2:30-5:00 Watch Contact (150 minutes) Pick up your pink sheets on the way out – just keep them in your portfolio with your lab worksheets

Looking ahead Look at Moodle:

Review resonant wavelengths How many waves fit in the length L of a guitar string?

Review resonant wavelengths How many waves fit in the length L of a guitar string? Use that to find the resonant wavelengths n How are these related to the frequency and the speed of oscillations of the guitar string? v = f

Example from workshop: Mandolin Ref: Negative Nancy and the Newtrons, Workshop 2, week 3 DATA/OBSERVATIONS: λ cm f Hz notesfundamental1/4 th length½ length1/3 length speed

Mandolin fundamental and harmonics ¼ above open A string Graph of octave above A string

Speed of string oscillations λ cm f Hz notesfundamental1/4 th length½ length1/3 length Speed (m/s) 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?

Resonant wavelengths for wind instruments Simple approximations from last week: (e.g. clarinet) (e.g. flute)

Clarinet: tube “closed” on reed end Johnston, Measured Tones (in Moodle LecturesAndReadings) However, opening and closing combinations of holes makes complex changes to “resonant wavelength” You might expect that

More complex instruments: Rigden, Physics and the Sound of Music (in Moodle LecturesAndReadings) Stretched membranes (drums)

Speed and wavelength depend on medium Frequency = constant = speed / wavelength Ex: Pluck open A string → mandolin 440 Hz ( 157 m/s string oscillations ) → drives air 440 Hz ( with m/s sound speed in air speed, & longer wavelength than mandolin’s )