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velocityofsound

velocityofsound - Nicholas J Pinto and Claudio Guerra-Vela...

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Unformatted text preview: Nicholas J. Pinto and Claudio Guerra-Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved (2006) 1 Experiment 10 VELOCITY OF SOUND IN AIR – RESONANCE TUBE Reference: Physics Laboratory Experiments – J. D. Wilson, DC Heath and Co. Objective To measure the velocity of sound in air at room temperature Theory Mechanical systems generally have one or more natural vibrating frequencies. When a system is driven at a natural frequency, there is a maximum energy transfer and the vibration amplitude increases to a maximum. In these conditions we say that the system is in resonance with the driving source and refer to the particular frequency at which this occurs as a resonance frequency . From the relationship between the frequency f , the wavelength ? , and the wave speed v , which is v = ? f , if the frequency and wavelength are known, the wave speed can be determined. Or, if the wavelength and speed are known, the frequency can be determined Figure 10-1 A pipe of length L closed at its bottom end and opened at its upper end showing the fundamental or first harmonic standing sound wave Air columns in pipes or tubes of fixed lengths have particular resonant frequencies. The interference of the waves traveling down the tube and the reflected waves traveling up the tube produces longitudinal standing waves, which must have a node at the closed end of the tube and an anti-node at the open end of the tube. The resonance frequencies of a pipe or tube depend on its length L . As shown in Figure 10-1, and 10-2 a certain number of wavelengths or “loops” that can be “fitted” into the tube length with the node- anti-node requirements. Since each loop corresponds to one half-wave length, resonance occurs when the length of the tube is nearly equal to an odd 2 number of quarter wavelengths i.e. L = λ /4, 3 λ /4, 5 λ /4, etc, or in general, L = n ?/4, n = 1, 3, 5, etc 1 Nicholas J. Pinto and Claudio Guerra-Vela. Department of Physics and Electronics. University of Puerto Rico at Humacao. Sponsored by the National Science Foundation (NSF) © All rights reserved (2006) 2 Or ? = 4 L / n 2 Incorporating the frequency, f and the speed, v through the relationship ? f = v , 3 Also called dispersion relation, f = v/ ? , and we have: f n = nv/ 4 λ , n = 1, 3, 5, etc 4 These f n frequencies are the resonance frequencies for all of the standing waves that can vibrate in the pipe Figure 10-2 A pipe of length L closed at its bottom end and opened at its upper end showing the second harmonic standing sound wave Hence, an air column (tube) of length L has particular resonance frequencies and will be in resonance with the corresponding odd-harmonic driving frequencies. As can be seen from the above equation, the three experimental parameters involved in the resonance condition of an air column are f , v , and L . To study the resonance in this experiment, the length...
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velocityofsound - Nicholas J Pinto and Claudio Guerra-Vela...

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