Frequency of a wave

One of the important characteristics of any wave is its frequency, the number of oscillations per unit of time.

The most common unit used internationally to express the frequency of a wave is the hertz, symbolized by Hz, which is equivalent to one oscillation per second.

Thus, for example, to say that a violin string, placed in vibration by the musician, emits a sound wave of 440 Hz frequency (reads 440 hertz), means that this sound wave produced by the instrument performs 440 oscillations every second. .

Other elements of a wave

The periodic wave is characterized by some elements, which are:

  • Ridges: the highest points of a wave are the ridges.
  • Valley: the lowest points of a wave form the valleys.
  • Amplitude: is the distance from the position of the resting rope to a ridge or valley.
  • Wave-length: is the distance between two successive ridges or two successive valleys. We symbolize the wavelength by the Greek letter l.
  • Period: is the time taken to produce a complete oscillation (one cycle), that is, the time when the source generates one up and one down cycle.
  • Frequency: number of complete oscillations (cycles) generated per unit of time (minutes, seconds, etc.)
In the same propagation medium, the longest waves will have the lowest frequency and those of the highest frequency will have the shortest wavelength.

Remember if! The amplitude and frequency of a wave depend on the movement that gives rise to that wave (in the drawings, the movement of the hands that vibrate the rope).

Relating period and frequency

If a source produces a valley and a ridge every two seconds, the time interval for a complete cycle is 2 seconds; therefore, the period is 2s. In this case, how many complete oscillations (one ridge plus one valley) are generated every second?

The response is half oscillation, or half cycle, generated every 1s.

Therefore, the number of oscillations per second or frequency is 0.5 oscillation in one second. So if we call the T period, and the f frequency, In our example, we will have T = 2s and f = 0.5 cycle per second.

In the mathematical language:


In the International Measurement System (SI), the period unit is the second, and the frequency unit is the cycle per second, called hertz (Hz).

When we hear that a computer's processor is 2.1 gigahertz, it means that it processes 2.1 billion information per second. When we say that the frequency of a radio station is 99.7 megahertz, we are saying that the radio wave corresponding to that station has 99.7 million oscillations per second.