Frequency (f)

Frequency describes how often a repeating event or oscillation occurs per unit time. It is measured in hertz (Hz) in the SI system, where 1 Hz = 1 cycle per second. Frequency is a key parameter in wave phenomena, signal processing, and electromagnetic systems.

Relationship Between Frequency and Wavelength

Frequency and wavelength are linked by the wave propagation equation:

c = λ × f

Where:

• c = Speed of wave propagation (e.g., speed of light for EM waves)

• λ = Wavelength (meters)

• f = Frequency (hertz)

This relationship shows that frequency and wavelength are inversely proportional: as one increases, the other decreases.

Frequency Formulas

Periodic Motion:
For any periodic signal, frequency is the inverse of the period:

f = 1 / T

Where:

• T = Period of one complete cycle (seconds)

Angular Frequency:
Angular frequency (ω) is another representation used in physics:

ω = 2π × f

Where:

• ω = Angular frequency (radians per second)

• f = Frequency (Hz)

Example Calculation

A sound wave with a period of 0.005 seconds has a frequency of:

f = 1 / 0.005 = 200 Hz

This corresponds to a typical vocal tone in human speech.

Applications of Frequency

Frequency plays a central role in various fields:

• Electronics: Signal generation, filtering, and circuit design

• Telecommunications: Band definitions in radio, Wi-Fi, 5G, and satellite systems

• Medical Technology: Used in ultrasound, MRI, and diagnostic imaging

• Physics and Optics: Quantum states, resonance, and electromagnetic spectrum

• Acoustics and Music: Pitch perception, harmonic analysis, sound engineering

• Astronomy: Frequency-based analysis of cosmic radiation and spectral lines