# 08b - 8B ACOUSTIC AND ELECTRIC RESONANCES A INTRODUCTION...

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8B: Acoustic and Electric Resonances - 1 8B: A COUSTIC AND E LECTRIC R ESONANCES A. I NTRODUCTION : Often a system has natural frequencies of vibration. In the case of the column of air in the PVC tube we are studying, these natural frequencies are called the harmonic frequencies, f 1 , f 2 ,…. A vibrating source, such as the speaker, is said to drive the column of air. As the frequency , f , of the driver (speaker) is slowly varied, the amplitude of the driven system (air column) gets larger and larger until it reaches a peak at one of its own resonant frequencies, f 1 , f 2 ,…. Therefore, as we sweep the speaker frequency past one of the harmonic frequencies of the air column, we hear the increase in amplitude of the vibrating air column as an increase in loudness of the radiated sound from the tube. At resonance the driving system passes energy very efficiently on to the driven system and the amplitude of the driven system reaches a maximum called A max . (See Rossing, The Science of Sound , Ch. 4.) A graph of the amplitude as a function of frequency is shown here. Note that the resonant amplitude peaks at frequency f 1 and that the peak has a width, Δ f called the linewidth. The linewidth is usually measured at an amplitude of 71% of A max . For a system which loses energy rapidly through damping or friction, the maximum amplitude, A max , is small and the linewidth large, and the resonance is said to be broad . Similarly, for a resonating system which loses energy very slowly, the maximum amplitude is very large and the linewidth is very small. The resonance is said to be sharp.

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8B: Acoustic and Electric Resonances - 2 The quality, Q , characterizes the sharpness of one of the resonances. For example, for the fundamental frequency the Q value is: Q = f 1 Δ f . (1.0) A high Q system is one with a sharp resonance. Once set oscillating it loses energy very slowly. A tuning fork is an example of an object with a very high Q . To drive an object with high Q , the driving frequency must be very close to the resonant frequency, f 1 . B. M EASUREMENT OF THE Q OF A R ESONANCE : 1. High Q System: It is convenient to measure the Q of one of the harmonics of your long PVC tube with one end closed. If your tube does not already have one end closed, close it at described in the first part of the lab. a.
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08b - 8B ACOUSTIC AND ELECTRIC RESONANCES A INTRODUCTION...

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