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The operation is simple. Clap and the lamp turns on. Clap again and it turns off.
The electret microphone picks up the sound of your claps, coughs, and the sound of that book knocked off the table. It produces a small electrical signal which is amplified by the succeeding transistor stage. Two transistors cross connected as a bistable multivibrator change state at each signal. One of these transistors drives a heavier transistor which controls a lamp.
I built my prototype on a cardboard cover from an old notebook. Punched holes using dividers and placed the components down flat. It might look neater if you draw the circuit diagram on to the board before you begin. A photo is included below. The components are from my junk box and I found that it works even if you omit that 4.7 Megohm resistor. Your results may vary.
The transistor types are not critical and any n-p-n silicon transistors should work
A revised version
Based on the comments of the many people who built this circuit successfully, and the few who tried to and failed, the circuit was revised. Two changes, mainly: the filament lamp was replaced by a bunch of LEDs, and the output stage was coupled to the collector instead of the emitter of the bistable.
The sound of your claps is picked up using an electret microphone. Some people call it by the name "condenser microphone" which usually refers to exhorbitantly priced things intended for the recording studio. If you could buy yours and still have your shirt on your back relax - it's an electret mike all right. Inside it is an electret film - which is the electrical analogue of a magnet - stretched so that it will vibrate in sympathy with any sound falling on it. These vibrations cause the electrical charge on a perforated plate nearby to change, and a field effect transistor converts these into corresponding changes in current.
This microphone has a stage of amplification built in. The power for this built in amplifier is supplied by connecting a resistor to a positive source of voltage, and the changes in current get reflected as changes in voltage across this resistor according to the familiar relation V = I*R. A larger resistor will give you a larger voltage, but then, the current into the device gets reduced which brings down the gain. The value of 5600 ohms (usually abbreviated to 5.6K, and written down in schematics as 5K6) seems to work all right.
A transistor stage, biased near cut-off (that is, almost no current with no signal) amplifies the signal from the microphone. The output of the microphone is coupled to the base of the transistor using an electrolytic capacitor (note: using a better capacitor here will not work). The top of the electret microphone is at a few volts, the base conducts at around half a volt, so the leakage current of the capacitor (all electrolytic capacitors leak at least a little bit) will eventually cause the steady state condition in which the leakage of the capacitor goes into the base terminal of the transistor. So the collector will have Hfe times this leakage, which can usually be ignored.
The first time the microphone output goes positive, however, (because somebody clapped) this change gets coupled to the base entirely due to the action of the capacitor. This causes the current through the transistor to increase, and this increase in current causes the voltage at the collector, which was sitting near the supply voltage, to fall to nearly zero. If you clapped loudly enough, of course.
This is not a high fidelity audio amplifier. Its function is to produce no output for small sounds and large output for (slightly) bigger sounds, so the customary biasing network can be omitted. The 4.7 Megohm resistor in the previous version was as good as an open circuit, and its omission does not affect the operation of the clap switch in any way. Provided, of course, that you use that 10 microfarad electrolytic capacitor.
Two cross connected transistors in a bistable multivibrator arrangement make up a circuit that remembers. You can set it to one of two possible states, and it will stay in that state until the end of time. When one transistor conducts, its collector is near ground, and a resistor from this collector feeds the base of the other. Since this resistor sees ground at the collector end the base at the other end receives no current, so that transistor is off. Since this transistor is off, its collector is near supply potential and a resistor connects from this to the base of the other transistor. Since this resistor sees voltage, it supplies the base with current, ensuring that the transistor remains on. Thus this state is stable. By symmetry, the other state is, too.
On a clap, the state of the bistable changes. The output of the amplifier is converted to a sharp pulse by passing it through a (relatively) low valued capacitor, of 0.1 microfarads (100 nanofarads). This is connected through "steering" diodes to the base of the transistor which is conducting. This transistor stops conducting, and the other transistor was not conducting anyway. So at a clap, both transistors become off.
Then, those two capacitors across the base resistors come into action. The capacitor connecting to the base of the transistor which was ON has voltage across it. The capacitor connecting to the base of the transistor which was OFF has no voltage across it.
As the sound of the clap dies away, both bases rise towards the supply voltage. But, due to the difference in the charges of the two capacitors, the base of the transistor which was previously not conducting reaches the magic value of half a volt first, and it gets on, and stays on. Until the next clap.
Two red Light Emitting Diodes have been placed in the two collector circuits so that this circuit can be made to work by itself. If you cover up one LED, and display the other prominently, you have it there - a clap operated light.
In order to have a decent amount of light from this circuit, I propose to use six white LEDs in three groups of two each. Each series connected string of two LEDs is arranged to draw around fifteen milliamperes or so by using a series resistor of 330 ohms. Two LEDs in series will drop about five or six volts, and the remaining battery voltage drop across this resistor determines the current through the LEDs. You can get more brightness from the LEDs by reducing the value to 220 ohms or even 150 ohms, provided you keep within the ratings of the LEDs. Do so at your own risk.
Thus the output stage has to handle around fifty or sixty milliamperes. This will give you fairly long time of claplighting with a PP3 battery. The 100mA filament lamp seems to be somewhat hard to find, and people were using torch bulbs, which run at much higher current, and killing their batteries in a few minutes.
A transistor gets its base driven from the collector of one of the transistors in the bistable. With this connection, due to the base current through it, one red LED in the bistable switches between half bright and full, and the other switches between fully off and on. This is normal.
Because the LEDs do not draw as much current as a filament lamp, the output transistor, too, can be of the common small signal variety. All four could be any small signal n-p-n transistor and the circuit should work. So would it with four p-n-p transistors, provided you switch the polarity of every (polarised) component