The frequency is determined by the wave source. For example, throwing a stone into calm water will disperse water waves. In dispersed water waves, no matter how far away from the falling point, they all have the same frequency, but the farther away, the smaller the amplitude and the less energy.
There is no formula for the amplitude a of T= 1/f, in which the period is t (in seconds), the frequency is f (in hertz) and the amplitude is a (in meters), the frequency is equal to the reciprocal of the period, and the amplitude is related to the nature of the wave itself, so it has no formula with the other two.
Formation of sideband
When the amplitude of the carrier changes according to the modulation signal, an amplitude modulated carrier is generated. The waveform of this amplitude-modulated carrier is constant in frequency, and its amplitude varies with the modulated signal. But mathematically, it can be proved that AM carrier contains other frequencies besides carrier frequency. These frequencies are generated by the modulation program and form frequency bands, which are called sideband frequencies.
Use of sideband: sideband frequency is not only an abstract concept in mathematics. In fact, it can be separated from AM carrier and widely used in radio transmission systems.