7.1 - Oscilloscope traces and wave measurements

Time-base and frequency

Can the same sound appear to have a different frequency just because you turn a knob? Its trace can look stretched or squeezed, but the sound has not changed. You must read the oscilloscope's scales as well as the shape.

A cathode-ray oscilloscope, or CRO, displays a changing potential difference. The time-base sweeps the spot horizontally at a known rate while the input signal deflects it vertically. For a steady repeating signal, the screen shows a voltage–time graph. A triggered, stable display helps you identify corresponding points of successive cycles.

The time-base setting gives the time represented by each horizontal division, often in $\mathrm{ms/div}$ or $\mathrm{\mu s/div}$. A division may be a centimetre square on a CRO grid; use the scale actually stated.

For improved precision, measure several complete cycles across a large fraction of the screen and divide their total time by their number. Count intervals, not peaks: four successive peaks enclose three cycles.

For example, three cycles span 9.0 divisions at $0.10\,\mathrm{ms/div}$. Their total duration is $0.90\,\mathrm{ms}$, so $T=0.30\,\mathrm{ms}$ and $f\approx3.3\,\mathrm{kHz}$.

[DIAGRAM: asset_name: Reading an oscilloscope grid; asset_slug: cro-time-gain; caption: Count a complete cycle horizontally and measure amplitude from the signal's middle line; description: A sinusoidal CRO trace on a ten-by-eight division grid has period four horizontal divisions and amplitude two vertical divisions. A horizontal arrow marks one cycle and a vertical arrow marks amplitude from the middle line, with peak-to-peak height four divisions. The settings are time-base 0.20 milliseconds per division and vertical scale 0.50 volts per division.]

Vertical scale and amplitude

The CRO's vertical deflection represents input potential difference. Its calibrated vertical setting, commonly called y-gain, is often given as volts per division. Multiply a vertical distance on the grid by this setting to obtain a voltage difference.

The amplitude of a sinusoidal voltage is its maximum deviation from its middle value. The peak-to-peak voltage is the full difference between the positive and negative extremes, twice the amplitude.

On the diagram, the amplitude is two divisions. With $0.50\,\mathrm{V/div}$, it is $1.0\,\mathrm{V}$; the peak-to-peak voltage is $2.0\,\mathrm{V}$. Taking the full four-division height as the amplitude would double the result.

A microphone supplies an electrical signal related to sound. The CRO measures that signal's voltage amplitude. It cannot directly tell you the air-particle displacement or pressure amplitude without a suitable calibration. Likewise, a displacement sensor's voltage must be converted using its stated response.