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# Exponential Function

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An example of an exponential function is the voltage as a function of time Vf(t) as the capacitor C1 discharges from an initial voltage Vi to a resistive load R1. The circuit of this is shown below

Figure 1. Discharge of Capacitor

Where

Vf is the final voltage

Vi is the initial voltage across the C1

 Time Calculated Value Oscilloscope Reading 0.05 7.278 7.300 0.10 4.415 4.500 0.15 2.678 2.700 0.20 1.624 1.700 0.25 0.985 1.000 0.30 0.597 0.700 0.35 0.362 0.400 0.40 0.220 0.200 0.45 0.133 0.100 0.50 0.081 0.000

Table 1. Calculated and Oscilloscope Voltages

Figure 2. Calculated Voltages

Figure 3. Oscilloscope Voltages

Logarithmic Function

An example of an logarithmic function is the Sound Pressure Level which is expressed in decibels.

SPL = 20 log(P/P0)                        (dangerousdecibels.org, 2005)

Where:

SPL     is the sound pressure level in decibels

P0        is the reference threshold of hearing, 2 x 10-5 N/m2

P         is the measured pressure amplitude in N/m2

 P SPL Calculated Measured 0.00001 -6.021 -6.000 0.00005 7.959 8.000 0.0001 13.979 14.000 0.0005 27.959 28.000 0.001 33.979 34.000 0.005 47.959 48.000 0.01 53.979 54.000 0.05 67.959 68.000 0.1 73.979 74.000 0.5 87.959 88.000 1 93.979 94.000 5 107.959 108.000 10 113.979 114.000 50 127.959 128.000 100 133.979 134.000

Table 2. Calculated and Measured Sound Pressure Levels

Figure 5. Calculated Sound Pressure Levels

Figure 6. Measured Sound Pressure Levels

Appendix

References

”Sound Measures”. DangerousDecibels.org website: http:// www.dangerousdecibels.org/teachers_guide/DDB_TRG_Activities_10.pdf on May 1, 2007

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