Tricky Circuit

Frequency, pulse shape and pitch

Build a tone from two levels

Pitch is how high or low a sound seems. Frequency f counts cycles per second; Hz (hertz) means one cycle per second. A rectangular wave switches between 0 and V; at 50% duty it is a symmetric square wave. Duty D is the percentage spent high. Period T lasts one cycle; ms is millisecond, 1/1000 second.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

Piezo means piezoelectric: voltage changes a material’s shape so it can vibrate and make sound. The lab models electrical timing and mean voltage, not piezo loudness or current. Optional playback is a short browser tone, not a physical piezo model. Devices may sound different at the same frequency.

Piezo is short for piezoelectric: a material changes shape with voltage and can vibrate air into sound. Here V is the high level in volts, D the high-time percentage and Vmean the time average. Changing D changes pulse shape, not f. At 50% both levels last equally long.

Difficulty

  1. Build · Build it

    Power on with f = 200 Hz, D = 50% and V = 5 V. Get T = 5 ms and Vmean = 2.5 V.

    Need a hint?

    f = 200 Hz; D = 50%; V = 5 V → T = 5 ms; Vmean = 2.5 V

  2. Explore · Change the command

    Set f = 1000 Hz, D = 25% and V = 5 V. Get T = 1 ms and Vmean = 1.25 V.

    Need a hint?

    f = 1000 Hz; D = 25%; V = 5 V → T = 1 ms; Vmean = 1.25 V

  3. Solve it · Solve the challenge

    Set f = 500 Hz, D = 75% and V = 4 V. Get T = 2 ms and Vmean = 3 V.

    Need a hint?

    f = 500 Hz; D = 75%; V = 4 V → T = 2 ms; Vmean = 3 V

Extra reading and circuit recipes

Build a tone from two levels

One repeated on-and-off pattern can become a beep. First predict its timing on the trace; then, if browser playback is available, listen to the frequency.

T = 1000 / f ms; Vmean = V × D / 100

One cycle is high for D% of its duration and zero for the rest. The average is V times that fraction. Frequency controls cycle timing; the acoustic response also depends on the sound device.

A useful pattern

Doubling frequency halves period: 200 Hz has 5 ms cycles, while 400 Hz has 2.5 ms cycles. Neither change requires a different pulse height.

Beyond the model

A real piezo has mechanical resonances and a frequency-dependent response. Mean electrical voltage alone cannot tell you its sound level.

A useful trap to avoid

A 2.5 V mean does not mean the wire stays at 2.5 V: this waveform alternates between 0 and 5 V. More mean voltage is not a universal rule for a louder tone.

Keep f = 200 Hz and V = 5 V, but change D from 50% to 25%. What happens?

  1. T stays 5 ms; Vmean becomes 1.25 V
  2. T becomes 2.5 ms
  3. frequency becomes 100 Hz
Read more

Duty shortens high time within the same cycle. The mean falls, but the cycle frequency is unchanged.

Build it

Set 200 Hz, 50% and 5 V. Equal high and low intervals give a 2.5 V mean.

f = 200 Hz; T = 5 ms; Vmean = 2.5 V

Change the command

Set 1000 Hz, 25% and 5 V. The cycle is 1 ms long, high for 0.25 ms, with a 1.25 V mean.

f = 1000 Hz; T = 1 ms; Vmean = 1.25 V

Try another path

Keep 5 V and 50%, compare 200 and 400 Hz, and predict the period first. Then hold frequency fixed and change duty: distinguish pulse shape from repetition rate.

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