What's the relationship between frequency and phase?

Frequency is the speed of oscillation, the phase is to appear sooner or later suggested to learn trigonometric functions and harmonic vibration, which has to speak frequency and phase. All these have been learned, but still do not understand. Two sine waves if the frequency is different is not the phase must be different? I think if you want to compare the phase of the two waveform, the premise should be two waves to the same frequency, but not the same, because the phase detector two input frequency is different. So I'm very confused now. If the frequency is different, the phase difference time is changed. After the phase-locked loop is stabilized, the two input frequencies of the phase detector are the same, and the phase difference remains constant. Take the sine function as an example f (t) = sin (2πft + α): f is the frequency; 2πft + α is phase; α is the phase of T = 0 o'clock, which is the initial phase. Frequency is not the difference between the frequency and phase is the period of two independent parameters of the park function, imagine two people around a circular field to run, from the starting point of the arc distance is the movement position and the starting point Clip Center angle function, this angle is the phase, and a certain time the number of laps is the frequency, If the two people at the same speed (that is, the same frequency), the distance between the two is always the same, that is, the phase difference is certain, the difference in size depends on the rear runner than the first runner to postpone the start of time. If the two people are not the same speed, then the distance (phase difference) is constantly changing. So the frequency is different, the phase difference is not fixed. Phase detector, no matter the frequency is only compared to phases, as long as the phase change, give the signal to the controller frequency control, so that the frequency of the same. "F (t) = sin (2πft + α): f is the frequency; 2πft + α is phase; α is the phase of T = 0 o'clock, which is the initial phase. "It's so simple. First of all, we usually say that the word "phase" actually has two meanings: first, the first phase of the periodic signal, the general sense of the phase, that is, the "instantaneous phase" frequency and phase, the beginning is the properties of the periodic signal, the frequency is the number of cycles per unit of time, the initial phase refers to the period signal relative to the The instantaneous phase refers to the period in which the signal "goes to a cycle" at any one time. For the above formula, if mathematically understood: the frequency is the phase of the differential (phase of the "travel speed") or the phase is the frequency of the integral. This relationship, from the mathematical promotion of a step, even if the F is a variable also set up, and then back to the physical world, it is found that do not have to force "strict" periodic signal, the frequency and phase can be instantaneous values. The "phase" of the so-called phase detector refers to this instantaneous phase, so nature does not have to be limited to periodic signals, and of course it does not have to be confined to the "same frequency" signal, otherwise "phase detector" is a wrong word. Phase detector function, in theory, this instantaneous phase difference into a voltage value (of course, the actual circuit will take a period of time to obtain results, it is impossible to completely "instantaneous"). The phase-locked loop works by using the output of the phase detector to control the frequency of the VCO, but the actual phase control is achieved by the integral of the instantaneous frequency, which ultimatelyThe difference between the instantaneous phase of the feed-back and the instantaneous phase of the input tends to zero. 

What is the relationship between frequency and phase