harmonics lab

# harmonics lab - Labs IIa and IIb Harmonics and Intervals...

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Labs IIa and IIb – Harmonics and Intervals Physics of Music and Color Kelsey Schur September 27 th , 2007 Introduction In Labs IIa and IIb, students investigated various properties of excited strings. Lab IIa employed electronic equipment to study the properties of vibrating strings, while Lab IIb was strictly acoustic. There were four goals in the first part of the lab. Students were to study the relationship between the fundamental frequency of a vibrating string, the tension, and the linear mass density. Also, they were to study the resonant excitation of a string by an electromagnetic coil. Thirdly, students needed to identify the harmonic components of the excited string's sound. Finally, using an oscilloscope pattern, students made a harmonic analysis of the sound of a bowed string. In the second part of the lab, students used an acoustic sonometer to identify the harmonic components of the strings' sounds. They studied the relationships between consonant musical intervals, numerological characteristics of standing waves, and resonances. For the first part of the lab, it is important to understand the mathematics that will be used to determine the tension of the string on the PASCO sonometer and the frequency and period of the wave when the string is excited. To calculate tension ( T ), one needs to know the notch (n) on the PASCO sonometer where the weight which determines tension has been hung. The slot nearest the string is numbered 1, and the slot furthest is 5. The student also needs to know the force of the weight of gravity (g), which is 9.8 N/kg. Lastly, it is also necessary to know the weight of the mass (m) suspended from the bar at the end of the sonometer. These values can then be used calculate the tension using the following equation: T = nmg Information from the oscilloscope can be used to calculate the period (T) of the wave. First, the

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experimenter must know the sweep rate that the oscilloscope has been set to. The sweep rate (r) is the scale of the wave pattern displayed on the screen. Once you know the sweep rate, you simply multiply it by the number of divisions (d) of the scale that one cycle of the wave extends over. T = rd From here, it's easy to calculate frequency, because frequency is simply the inverse of the period: f = 1/T Results 6.1)d) Notch Tension, T (N) T (√N) Frequency, f (Hz) 1 9.8 N √9.8 = 3.13 √N 1/(4.5(2.5)) = .0889 Hz 2 19.6 N √19.6 = 4.427 √N 1/ (3(2.5)) = .1333 Hz 3 29.4 N √29.4 = 5.422 √N .16 Hz 6.1)e)
6.3)f) String Diameter, d (mm) 1/diameter, 1/d (1/mm) Frequency, f (Hz) 1 .45 mm 1/.45 mm .357 Hz 2 .6 mm 1/.6 mm 1/3 Hz Discussion Lab IIa, Familiarization First, students needed to become acquainted with the equipment. The first task was to pluck the

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## This note was uploaded on 03/29/2008 for the course PHY 10 taught by Professor Gunther during the Spring '08 term at Tufts.

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harmonics lab - Labs IIa and IIb Harmonics and Intervals...

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