Sonometer-02-03-2018.pdf

# Sonometer-02-03-2018.pdf - Sonometer Equipment Capstone...

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Sonometer Equipment Capstone, sonometer (with detector coil but not driver coil), voltage sensor, BNC to double banana plug adapter, set of hook masses, and 2 set of wires CAUTION In this experiment a substantial mass, supported by a wire, hangs over the floor. If the wire should break the mass will fall to the floor. PLEASE KEEP YOUR FEET AWAY FROM UNDERNEATH THE MASS. 1 Introduction The experiment uses a PASCO Sonometer to measure how normal mode frequencies of metal wires fixed at both ends vary with length, mode number, tension, and mass per unit length of the wires. A sonometer (or monochord) is a device that holds a single wire under a desired tension and can detect the normal mode vibrations of a wire. 2 Theory A string that is struck will vibrate in several harmonics at once. The fundamental harmonic will resonate with the greatest amplitude and will be accompanied by several lower harmon- ics. In this experiment you will observe and determine the fundamental harmonic when you change the length of string and wire tension. The sonometer has a string that is held at two adjustable ends that can be fixed. When the string is plucked, it will vibrate in its fundamental mode along with multiple modes of its fundamental harmonic. The wire tension is T and can be varied by using different masses. Distance along the wire is denoted by x and distance transverse to the wire by y . Dispersionless waves propagate in the positive or negative x direction with the velocity v = p T/μ , where μ is the mass per unit length. For a fixed wire that has a length of L, the time required for the fundamental harmonic to oscillate from the initial fixed end to the other and back, will be related to speed the wave propagates and two times the length between each end (2 L ). The total length will be equal to the fundamental harmonic wavelength. Higher order fundamentals will occur when the wave propagates from one end to the other with λ of 2, 3, 4, etc. On the next page there is an image of the spectrum you will be viewing on Capstone. When you strum the string, the fundamental harmonic, as well as higher order modes, will oscillate. 1

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General Physics I Lab: Sonometer Image Credit: Rossing, Moore, and Wheeler, The Science of Sound,(San Francisco: Addison Wesley), 2002 In the figure above you can see the initial response of strumming the string for first seven modes. The normal mode wavelengths are then λ n = 2 L n ( n = 1 , 2 , 3 , . . . ) The speed of the fundamental harmonic will be related to the frequency and the wavelength. This means normal mode frequencies of the string can be determined with v = combined with the equation of the fundamental modes λ n = 2 L n and the speed the wave propagates v = p T/μ .

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