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).
Let 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:
Each 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)|
|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.
The 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.
1. What is the frequency of an X-ray (wavelength 0.5nm)?
2. A sound wave, with a frequency of 44 kHz, has a wavelength of 7.7mm. What is the speed of sound?
3. What is the fundamental frequency of the following signal?
4. Approximately how many harmonics does it contain?
5. The three sine waves sin x°, 4sin(2x-50)° and 0.5sin(3x+120)° are added together to form a signal. What are the frequencies of each of the waves? What is the signal's fundamental frequency? Assume that the waves are travelling at the speed of light, and that 60° = 1mm.