See a wave the way an engineer does
Set a signal on the generator, then read it on the scope. Turn the knobs (drag, scroll or use the arrow keys) and the notes underneath explain exactly what the screen is telling you.
Timing
Voltage
Trigger
The ideas behind the trace
Eight short lessons. Each one has a button that sets up the bench so you can see the idea for yourself.
fFrequency and periodHow often a wave repeats
Frequency (f) is how many complete cycles happen every second, measured in hertz (Hz). Period (T) is how long one cycle takes. They are two views of the same thing.
Prefixes you'll meet: 1 kHz = 1,000 Hz, 1 MHz = 1,000,000 Hz, 1 GHz = 1,000,000,000 Hz. Going the other way, 1 ms = 0.001 s and 1 µs = 0.000001 s.
On a scope you never read frequency directly off the grid. You count how many divisions one cycle takes, multiply by TIME/DIV to get T, then work out f = 1/T.
VAmplitude: peak, peak-to-peak and RMSThree ways to say "how big"
Peak (Vpk) is from the centre line to the top. Peak-to-peak (Vpp) is from the bottom to the top, so it's twice the peak for a symmetrical wave. RMS is the equivalent DC voltage that would heat a resistor by the same amount. Meters and mains ratings use RMS.
| Waveform | Vrms |
|---|---|
| Sine | Vpk ÷ √2 ≈ 0.707 × Vpk |
| Square (±Vpk) | Vpk |
| Triangle or ramp | Vpk ÷ √3 ≈ 0.577 × Vpk |
The energy a wave carries goes with amplitude squared (E ∝ A²). Double the amplitude and you get four times the power into the same load.
λWavelengthHow long one cycle is in space
A scope shows a wave in time. Out in the world a wave also has a size in space: the wavelength λ (lambda), the distance from one crest to the next.
Radio and light travel at c ≈ 300,000,000 m/s. Sound in air travels at about 343 m/s. The same frequency gives wildly different wavelengths depending on what's carrying it.
Wavelength sets antenna sizes: a quarter-wave antenna for 2.4 GHz Wi-Fi is about 3.1 cm. Use the calculator further down to try your own.
φPhaseWhere in the cycle you are
One full cycle is 360°. Phase tells you how far through that cycle a wave is at a given moment, or how far one wave is ahead of another with the same frequency.
Phase matters everywhere in AC: in a capacitor the current leads the voltage by 90°, in an inductor it lags by 90°, and three-phase supplies use three waves spaced 120° apart to drive motors smoothly.
∿Waveform shapesSine, square, triangle and ramp
- Sine: the natural shape of anything that rotates or oscillates. Generators, mains power and radio carriers are sine waves.
- Square: switches between two levels. Digital clocks, logic signals and PWM are square waves.
- Triangle: ramps up and down at a steady rate. You get one when a capacitor is charged by a constant current.
- Ramp (sawtooth): rises steadily, then snaps back. A scope's own timebase is a ramp: it sweeps the trace left to right, then resets.
The harmonics lab below shows how square, triangle and ramp waves are really stacks of sine waves.
DDuty cycle and PWMControlling power with a square wave
Duty cycle is the fraction of each period that a square wave spends high. PWM (pulse-width modulation) changes the duty cycle to control average power without wasting energy as heat.
analogWrite(pin, 64) gives about 25% duty. On a 5 V pin the average is 0.25 × 5 = 1.25 V. On most Uno pins the PWM frequency is about 490 Hz.The same idea runs LED dimmers, fan controllers and the variable frequency drives that run industrial motors, which switch at several kHz.
dBDecibelsComparing signals on a log scale
Decibels compare two levels using a logarithm, which keeps huge ranges manageable.
Power: dB = 10 × log₁₀(P₂ / P₁)
- +6 dB ≈ double the voltage; −6 dB ≈ half.
- −3 dB = half the power. Filter "cut-off frequencies" are the −3 dB points.
- +20 dB = ten times the voltage (100 times the power).
TTriggeringWhy the trace stands still
A scope draws the signal over and over, dozens of times a second. If each sweep started at a random point in the cycle, every picture would be shifted and the trace would look like a smear.
The trigger fixes this: the scope waits until the signal crosses the trigger LEVEL going up (a rising edge), and starts every sweep from exactly that point. Same starting point each time means a rock-steady picture.
If the level is set above the highest point of the signal, the signal never crosses it. The scope gives up waiting and free-runs in AUTO mode, and the trace starts to wander.
Harmonics lab: building waves from sines
Any repeating wave can be built by adding sine waves at whole-number multiples of its frequency. This is Fourier's idea, and it's why a square wave on a cheap speaker sounds buzzy rather than pure.
The faint line is the ideal shape. The bright line is the sum so far. The bars show how strong each harmonic is: 1 is the fundamental, 3 is three times its frequency, and so on.
Wavelength calculator
Enter a frequency and pick what the wave travels through. Useful for antenna lengths, cable runs and speaker placement.
Real antennas are usually trimmed a few percent shorter than the calculated quarter-wave because of end effects and the thickness of the element.
The electromagnetic spectrum
Radio, light and X-rays are the same thing at different frequencies. The bar uses a log scale: each step along it is ten times the frequency of the last. Visible light is the thin rainbow sliver.
Where you'll meet these frequencies
From the workshop to the airwaves, a quick reference of real signals and why they sit where they do.
| Signal | Frequency | Why it matters |
|---|---|---|
| Mains power | 50 Hz (IE, UK, EU) · 60 Hz (US) | Sets the speed of AC motors and the 100/120 Hz ripple you'll see after a rectifier. |
| Human hearing | 20 Hz – 20 kHz | The upper limit drops with age. Audio gear is designed around this range. |
| Telephone voice | 300 Hz – 3.4 kHz | Enough for speech to be understood, which is why phone calls sound thin. |
| Arduino PWM | ≈ 490 Hz / 980 Hz | Default analogWrite frequency on an Uno (pins 5 and 6 run at 980 Hz). |
| VFD motor switching | 2 – 16 kHz | Higher carrier frequency means quieter motors but more switching heat in the drive. |
| Ultrasonic sensor | 40 kHz | HC-SR04 style sensors time a 40 kHz echo to measure distance. |
| AM radio | 531 – 1602 kHz | Long waves bend around the Earth, so AM carries far, especially at night. |
| FM radio | 87.5 – 108 MHz | Roughly line of sight, but better audio quality and less noise than AM. |
| Wi-Fi and Bluetooth | 2.4 GHz · 5 GHz · 6 GHz | Higher bands carry more data but get through walls less well. |
| Microwave oven | 2.45 GHz | Water molecules absorb energy well at this frequency. It's also a band licensed for industrial use, which is why Wi-Fi shares it. |
| Visible light | ≈ 400 – 790 THz | Red is the lowest frequency we can see, violet the highest. |
Check yourself
Six questions. Pick an answer to see the explanation.
Formula sheet
f = 1 / TFrequency from periodv = f × λWave speed, frequency and wavelengthVrms = Vpk / √2RMS of a sine waveVpp = 2 × VpkPeak-to-peak of a symmetrical waveT = divs × TIME/DIVReading period off a scopeV = divs × VOLTS/DIVReading voltage off a scopeVavg = D × VhighAverage of a PWM signaldB = 20 log(V₂/V₁)Voltage ratio in decibelsE = h × fPhoton energy (h = 6.626 × 10⁻³⁴ J·s)