Mathematical amplitude usually refers to the maximum deviation of fluctuation, that is, the distance between peak and trough. It is one of the important parameters to express the strength, power and energy of waves. The greater the amplitude, the higher the intensity and energy of the wave, and vice versa. For example, the higher the amplitude of sound waves, the louder the sound.

Frequency refers to the number of times in each period of fluctuation, usually expressed in hertz (Hz). The higher the frequency, the shorter the cycle time and the denser the fluctuation. For example, high-pitched instruments have higher frequencies than low-pitched instruments because they produce faster fluctuations.

In physics and engineering, amplitude and frequency are important parameters of many phenomena, such as mechanical vibration, electromagnetic waves, optics, astronomy and so on. Understanding and applying these two parameters can help us to better explain and describe many phenomena in nature. For example, by understanding the amplitude and frequency of seismic waves, we can better understand and predict the nature and influence of earthquakes.