Sinusoidal Wave

A sinusoidal wave (or sine wave) is a smooth, repetitive oscillation that follows the mathematical function:

y=Asin⁡(ωt+ϕ)y = A \sin(\omega t + \phi)

where:

• AA = Amplitude (maximum displacement)
• ω\omega = Angular frequency (2πf2\pi f, where ff is frequency)
• tt = Time
• ϕ\phi = Phase angle (determines wave shift)

Characteristics of a Sinusoidal Wave

1. Amplitude (AA) – The peak value of the wave, representing maximum displacement.
2. Wavelength (λ\lambda) – The distance between two consecutive peaks or troughs.
3. Frequency (ff) – The number of cycles per second, measured in Hertz (Hz).
4. Period (TT) – The time taken for one complete cycle (T=1fT = \frac{1}{f}).
5. Phase (ϕ\phi) – The initial angle determining the wave’s starting position.

Examples of Sinusoidal Waves

• Sound waves (pure tones in music)
• Light waves (electromagnetic waves in sinusoidal form)
• Alternating Current (AC) electricity
• Vibrations in mechanical systems

Sinusoidal waves are fundamental in physics, engineering, and signal processing due to their natural and smooth oscillatory nature.