A sine wave is a mathematical curve that represents a smooth oscillation or periodic oscillatory motion. It is defined by the trigonometric function sine (sin), hence its name.
The equation for a sine wave is typically written as:
y = A * sin(ωt + φ)
In this equation, A represents the amplitude, which determines the maximum displacement of the wave from its equilibrium position. ω (omega) represents the angular frequency, which determines the rate at which the wave oscillates. t represents time, and φ (phi) represents the phase shift, which determines the horizontal displacement of the wave.
A sine wave is periodic, meaning it repeats itself identically over regular intervals of time. The period of a sine wave is the time it takes for one complete cycle of oscillation. The period is determined by the angular frequency ω, and it is given by the equation:
T = 2π/ω
where T represents the period.
The periodic nature of the sine wave arises from the trigonometric nature of the sine function. The sine function is periodic itself, with a period of 2π. As a result, any function that is based on the sine function, such as a sine wave, will also be periodic.
It's worth noting that the sine wave is just one example of a periodic wave. There are other types of periodic waves, such as square waves or triangular waves, each with their own distinct shapes and mathematical representations.