Maths That Predicts Behaviour
Trigonometry & Waves
13 min · 2 worked examplesStudent plan
Sine waves, frequency and period, peak versus RMS, and why mains is quoted as 230 V when it peaks at 325 V.
After this lesson you can
- Resolve a force or a velocity into components
- Read amplitude, period and frequency off a waveform
- Connect a rotating angle to a sine wave
The sine wave
Rotate a point steadily around a circle and plot its height against time: you get a sine wave. That is not an analogy, it is the definition, and it is why alternating current from a spinning generator is sinusoidal.
Three numbers describe it completely. Amplitude is the peak height from the centre line. Period T is the time for one full cycle, in seconds. Frequency f is how many cycles happen per second, in hertz.
Period and frequency are reciprocals: f = 1 ÷ T. A 50 Hz mains cycle takes 1 ÷ 50 = 0.02 s = 20 ms. A 1 kHz tone takes 1 ms. Getting fluent at flipping between these two is worth more than it sounds, because datasheets quote one and your oscilloscope shows the other.
In the full lesson
- The sine wave
- Peak, peak-to-peak and RMS
- Phase
This lesson comes with the Student plan. The first module of Maths for Engineers is free.