Waveform Lab

Sine, triangle, sawtooth and square — with peak, peak-to-peak, RMS, mean and period marked on the trace itself. Then see where wavelength actually lives, build a shape out of harmonics, and find out why a cheap multimeter misreads three of the four.

Waveform

Peak Vp10 VFrequency f50 HzPhase0 °DC offset0 V

Every quantity marked on the trace itself, in its own colour.

Second trace

10.00 V

Vpp

20.00 V

V rms

7.07 V

Mean

0.00 V

20.00 ms

314 rad/s

Reading a waveform

Four numbers describe any periodic signal, and they are not interchangeable. Peak is the height above zero. Peak-to-peak is trough to crest, so it is twice the peak for a symmetric wave. RMS is the DC voltage that would heat a resistor equally — the one that matters for power. The mean is the DC component, which is zero for a symmetric wave and non-zero as soon as you add an offset.

Why RMS is not just “0.707 times the peak”

That factor is specific to a sine. A triangle of the same height has an RMS of 0.577 of its peak, and a square has the full peak — so at identical peak voltage a square heats a resistor about three times harder than a triangle in terms of power. The Compare tab puts the four side by side.

Period is not wavelength

On a voltage-versus-time plot the repeating interval is the period, measured in seconds. Wavelength is a distance, and you cannot get one from the other without knowing how fast the wave travels. That is why the Wavelength tab asks for a medium: the same 100 MHz signal is 3 m long in free space but only about 2 m inside RG-58 coax, because the cable slows it to 66 % of light speed.

Learn more → AC Fundamentals — Learn

Quick experiments

Watch RMS move but peak-to-peak stay put. Turn the DC offset up. The trace slides upward, the mean line follows it, and the RMS rises — but Vpp never changes, because it only measures trough to crest.
Compare heating at equal peak. Set 10 V peak and step through the four shapes on the Compare tab. RMS runs 10 V for the square, 7.07 V for the sine and 5.77 V for the triangle — the same height doing very different work.
Find the duty cycle that does not change RMS. Pick the square and sweep duty from 5 % to 95 %. The mean swings from −9 V to +9 V while the RMS stays at 10 V, because the magnitude is 10 V for the whole cycle either way.
Build a square from sines. On the Harmonics tab pick the square and drag from 1 to 40 terms. The edges sharpen but never stop overshooting — that stubborn 9 % ripple is the Gibbs phenomenon.
See a wavelength shrink inside a cable. Set 100 MHz and switch the medium from free space to RG-58. The wavelength drops from about 3 m to 1.98 m, which is why coax stubs are cut shorter than the free-space quarter wave.

Formula reference

RMS of a sine: $V_{rms} = \frac{V_p}{\sqrt{2}} \approx 0.707\,V_p$
The factor that only applies to a sine.
RMS of a triangle or sawtooth: $V_{rms} = \frac{V_p}{\sqrt{3}} \approx 0.577\,V_p$
Both are linear ramps, so they share a factor.
RMS of a square: $V_{rms} = V_p$
The magnitude is Vp for the whole cycle, whatever the duty.
Period and frequency: $T = \frac{1}{f} \qquad \omega = 2\pi f$
50 Hz gives a 20 ms period.
Wavelength — needs a propagation speed: $\lambda = \frac{v}{f} = v\,T, \quad v = vf \times c$
vf is the velocity factor: 1 in free space, about 0.66 in RG-58.
Crest and form factor: $CF = \frac{V_p}{V_{rms}} \qquad FF = \frac{V_{rms}}{V_{avg}}$
1.414 and 1.111 for a sine; 1.0 and 1.0 for a square.

Symbol	Meaning	Unit
$V_p$	Peak voltage, zero to crest	V
$V_{pp}$	Peak-to-peak, trough to crest	V
$V_{rms}$	Equivalent heating voltage	V
$\lambda$	Wavelength — a distance, not a time	m
$vf$	Velocity factor of the medium	—

Common mistakes

Using 0.707 × peak for every waveform.
That factor is the sine's alone. A triangle is 0.577 × peak and a square is the full peak. Using the sine factor on a square underestimates the heating by 30 %.
Trusting a cheap multimeter on a non-sine signal.
Average-responding meters measure the rectified mean and scale it by the sine form factor. They read about 4 % low on a triangle and about 11 % high on a square — opposite directions, so no single correction works. Use a true-RMS meter.
Calling the horizontal repeat distance a wavelength.
On a voltage-versus-time plot that interval is the period, in seconds. Wavelength is a distance and needs a propagation speed: λ = v/f. The two are only related through the speed of the medium.
Assuming a DC offset changes the peak-to-peak.
Offset moves the whole trace and changes the mean and the true RMS, but Vpp is trough to crest and is unaffected. This is exactly what AC coupling on a scope removes.
Expecting a square wave through a limited bandwidth to stay square.
The sharp edges are made of high harmonics. Remove them and the corners round off — which is why a square wave is the standard test for a channel's bandwidth.

Frequently asked questions

How do I calculate RMS voltage from peak?

It depends on the shape. For a sine, RMS is peak divided by the square root of 2, about 0.707 times peak. For a triangle or sawtooth it is peak divided by the square root of 3, about 0.577 times peak. For a square wave the RMS equals the peak.

What is the difference between period and wavelength?

Period is a time, the seconds taken for one cycle, and it is what you measure on a voltage-versus-time plot. Wavelength is a distance, how far the wave travels in one period, so it needs a propagation speed: lambda equals v divided by f. The two are only linked through the speed of the medium.

Why does my multimeter read the wrong value on a square wave?

Most inexpensive meters are average-responding: they measure the rectified mean and multiply by 1.1107, the form factor of a sine. That is exact on a sine but wrong elsewhere, reading roughly 4 percent low on a triangle and 11 percent high on a square. A true-RMS meter measures the heating effect directly and is correct on any shape.

Does a DC offset change the peak-to-peak voltage?

No. Peak-to-peak is measured from trough to crest, so shifting the whole waveform up or down leaves it unchanged. The offset does change the mean and the true RMS, and switching a scope input to AC coupling removes it.

Why does a square wave contain harmonics?

A square wave is the sum of a fundamental sine plus its odd harmonics, falling off as one over n. The sharp edges come entirely from the high harmonics, which is why a square wave passed through a limited bandwidth comes out with rounded corners.

What is crest factor?

Crest factor is peak divided by RMS. It is 1.414 for a sine, 1.732 for a triangle or sawtooth, and 1.0 for a square. It matters when choosing test gear and power components, because a high crest factor means brief tall peaks that can clip an input stage even when the RMS looks safe.