Hi Naveed's team leader,
You don't need to write a specification for the simple circuit of the Dancing LEDs project. Its operation depends entirely on the amount of sound level picked-up by its microphone. The sound level is determined by its power, closeness to the microphone and room acoustics.
1) Only C4 is charged by the recifying action of IC1B and D1. The charging current isn't limited by a resistor so is as fast as the small amount of output current from IC1B will allow. The output current of the opamp is spec'd from a minimum of 20mA, a typical of 40ma and no maximum but probably no more than about 50ma. The low-power opamp has a very slow slew-rate that also might limit the charge quickness of C4.
The charging speed of C4 doesn't matter anyway since the 4017 counter has a Schmitt-trigger action on its clock input, so it will trigger properly on any slow speed of input signal.
C4 is discharged only by R7, therefore the discharge time is 330n X 100K = 33ms.
2) The amplifying error of IC1A id determined by the accuracy of R4 and R5 since the opamp has an open-loop gain of about 30,000 at 30Hz. Its gain should be 1+(100K divided by 1K) = 101. IC1B has 100% negative feedback so its gain is exactly 1 for positive half-cycles of the output of !C1A.
3) IC1A amplifies frequencies above the high-pass filter action of the mic impedance in parallel with R1, R2 in parallel with R3, and C1. The amplification of low frequencies is also reduced by the high-pass-filter action of R4 and C2. The high frequency amplification of IC1A is limited by its low bandwidth and low slew rate and will drop above about 5KHz.
Since IC1A and IC!b have a combined gain of 101, the amplitude of the signal entering the counter is 101 times larger than the input, depending on frequency and tolerance of R4 and R5.
C5 is used to smooth the output voltage of the battery which will fluctuate wildly when the battery runs-down and its internal resistance increases. The recifier pulses of up to 50mA cause the wild voltage fluctuations without C5.
Did Naveed get the project working? He had a problem with its microphone. If he replaced the microphone, how does the project respond to music? Can you place its microphone far enough away from a speaker so that the LEDs step along in time to the music's beat? If the microphone is too close to a speaker are the LEDs a dim blur? Do the LEDs step along with each spoken syllable? ;D