LAB_9 - Time Varying 3 - Sound

LAB_9 - Time Varying 3 - Sound - Lab 9 Time-Varying Signals...

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Lab 9 99 Time-Varying Signals III - Sound Software Required Time Varying Signals Stack Summary Time-varying waveforms are fundamental phenomena in nature which manifest themselves in a variety of forms including thermal, mechanical, and electromagnetic. In many cases, these fluctuations can have a most profound effect on mankind and his artifacts. Therefore, an understanding of wave phe- nomena and the ability to measure them is of fundamental importance to all fields of engineering. In this experiment we will explore several important characteristics which many time-varying signals have in common by analyzing and synthesizing sound waves generated by a variety of sources. Educational Objectives After performing this experiment, students should be able to: 1 . Store and add signals on the oscilloscope. 2 . Operate a LabVIEW virtual "Harmonic Generator" on the laboratory computer. 3 . Control a signal generator using a LabVIEW virtual instrument. 4 . Synthesize and analyze arbitrary waveforms using the signal generator, computer and oscillo- scope. 5 . Observe and analyze the waveforms of sound waves generated by a variety of musical instru- ments and other sources. 6 . Observe, record and analyze the characteristics of their voices. "Science is the attempt to make the chaotic diversity of our sense-experience corre- spond to a logically uniform system of thought." - Albert Einstein
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Lab 9 100 Background Information 1. Waves and The Superposition Principle In many natural or "engineered" situations, we find that waveforms are simple harmonic functions which can be represented by a sinusoidal function. For example, the AC voltage in the home is almost an exact sine function as is the vertical motion of a piston in an automobile engine or the oscillations of the pendulum in a grandfather clock. Each can be described by the trigonometric function y ( t ) = A sin(2 π ft ), where A is the amplitude and f is the frequency of oscillation. Figure 1 displays the period and amplitude of a sine wave (in this case, voltage). The amplitude is equal to the peak voltage. The properties of a voltage sine wave can be measured in the lab. A frequency counter can mea- sure its frequency or period T = 1/ f . Most AC meters measure the RMS (root-mean-square) voltage of a wave. The RMS value of a periodic waveform is defined using the integral calculus as, Figure 1 - Sinusoidal Waveform. A = amplitude or peak voltage A-B = peak to peak voltage T = period = (1/ f ) f = frequency (cycles per second, Hertz) ω = frequency in radians = 2 π f –10 –5 0 5 10 246 81 01 2 x Peak Voltage A B Peak to Peak Voltage Period (T) V T Vtd t rms T = ) 1 2 0 (
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Lab 9 101 As you saw earlier, for a sine wave the above formula reduces to: Using an oscilloscope, the wave functions can be directly visualized and the amplitude A and period T found. Note that a DC voltmeter measures the average value of a function and thus would indi- cate zero in the case of the sine wave in Figure 1 which has a zero average value over a complete period.
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This note was uploaded on 12/16/2011 for the course ENGR 102 taught by Professor Cattell during the Fall '10 term at Community College of Philadelphia.

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LAB_9 - Time Varying 3 - Sound - Lab 9 Time-Varying Signals...

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