User:Inconspicuum/Physics (A Level)/Signal Frequencies
The frequency of a wave describes how many waves go past a certain point in one second. Frequency is measured in Hertz (usually abbreviated Hz), and can be calculated using the formula:
V = fλ
where V is the velocity of the wave (in ms-1), f is the frequency of the wave (in Hz), and λ (the Greek letter lambda) is the wavelength of the wave (distance from one peak / trough to the next, in m).
Multiple Frequencies
editLet us consider the following signal (time is in ms, and the y-axis represents volts):
This signal is constructed from a number of different sine waves, with different frequencies, added together. These sine waves are as follows:
Frequency Spectra
editEach of these sine waves has a different frequency. You can see this, as they have different distances between their peaks and troughs. These frequencies can be plotted against the amplitude of the wave, as in the table, and chart drawn from it, below:
| Wave (y=) | Period (ms) | Amplitude (V) | Frequency (Hz) |
|---|---|---|---|
| 3sin x | 6.284 | 3 | 159 |
| sin(0.5x + 40) | 12.566 | 1 | 80 |
| 2sin(3x - 60) | 2.093 | 2 | 478 |
This chart is known as the frequency spectrum of a signal.
Fundamental Frequency
editThe fundamental freqency is the lowest frequency that makes up a signal. In the above example, the fundamental frequency is 80 Hz. It is always the frequency farthest to the left of a frequency spectrum, ignoring noise. Other frequencies are known as overtones, or harmonics.