In the context of a sine wave, the terms "height" and "amplitude" are often used interchangeably to refer to the maximum displacement or magnitude of the wave from its equilibrium position. The amplitude represents the maximum distance from the equilibrium position that a particle or object undergoing the wave motion reaches.
Mathematically, the amplitude of a sine wave is half the difference between its maximum and minimum values. The height of the sine wave is simply the absolute value of the amplitude.
The relationship between the height and amplitude of a sine wave can be described as follows:
The height is equal to the amplitude when considering the absolute value, as the height represents the magnitude of the displacement from the equilibrium position without considering the direction.
The amplitude determines the overall scale or "size" of the sine wave. A larger amplitude will result in a taller or more pronounced wave, while a smaller amplitude will produce a shorter or less pronounced wave.
Doubling the amplitude of a sine wave will result in doubling the height as well, while halving the amplitude will reduce the height by half. The relationship between the two is linear.
It's worth noting that the terms "height" and "amplitude" may be used differently in specific contexts or fields, so it's always important to consider the specific definition and convention being used in a given situation.