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EXPERIMENT SOUND WAVES IN A RESONANCE TUBE Introduction: A wave is the propagation of a disturbance or energy and is characterized by its wavelength λ , the frequency of oscillation f (in Hz or 1/s = s 1 ), and the wave speed v . Sound wave is a longitudinal wave . When the diaphragm of a speaker vibrates, a sound wave is produced that propagates through the air. The sound wave consists of small motions of the air molecules toward and away from the speaker. The study of sound waves can be simplified by restricting the motion of propagation to one dimension, as is done with the Resonance Tube . A Standing wave occurs when a wave is reflected from the end of the tube and the return wave interferes with the original wave. The standing sound wave has displacement nodes and antinodes. These are points where the air does not vibrate, or vibrate with a maximum displacement, respectively. Reflection of the sound wave occurs at both open and closed tube ends. If the end of the tube is closed, the air has nowhere to go, so a displacement node must exist at a closed end. If the end of the tube is open, a displacement antinode exists at an open end of the tube. At certain frequencies of oscillation, all the reflected waves are in phase, resulting in a very high amplitude standing wave. These frequencies are called resonant frequencies . For an open tube (a tube open at both ends) with length L , resonance occurs when the wavelength satisfies the condition: L = n / 2 , n = 1, 2, 3, … (Open Tube) (1) For a closed tube (a tube open at one end), the condition is: L = n / 4 , n = 1, 3, 5, … (closed Tube) (2) Each successive value of n describes a state in which one more half wavelength fits between the ends of the tube. The first three resonance states for open and closed tubes are shown in Figure 1. Fundamental, n=1 First Overtone, n=2 Second Overtone, n=3 O p e n T u b e Fundamental, n=1 First Overtone, n=3 Second Overtone, n=5 C l o s e d ( a t o n e e n d ) T u b e Figure 1: Resonance States: Open and Closed Tubes The formulas and diagrams shown above for resonance in a tube are only approximate, mainly because the behavior of the waves at the ends of the tube (especially at an open end) depends partially on factors such as the diameter d of the tube and the frequency of the waves. The
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2 ends of the tubes are not exact nodes and antinodes. The following empirical formulas give a somewhat more accurate description of the resonance requirements for standing waves in a tube: Open Tube: L + 0.8 d = n λ / 2 , n= 1, 2, 3, … (3) Closed Tube: L + 0.4 d = n / 4 , n= 1, 3, 5, … (4) Important Notes When using the microphone to investigate the waveform within the resonance tube, be aware that the microphone is a pressure transducer . A maximum signal, therefore, indicates a pressure antinode (a displacement node) and a minimum signal indicates a pressure node (a displacement antinode). CAUTION
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This note was uploaded on 04/01/2011 for the course PHY 135 taught by Professor Wagihghobriel during the Spring '11 term at University of Toronto- Toronto.

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