According to t=t 1, when x=0, the derivative of y to time (vibration speed) =-A*2πu/λsin(φ)>0, and φ=-π/2 is determined.

There are two simple discrimination methods: one is to judge the upward direction according to the vibration direction. The other is that according to the image of the wave, along the propagation direction of the wave, we can see how many phases the wave needs to translate forward (or backward) to become a cosine wave, and that initial phase is how many phases need to be subtracted (or added). This problem requires the waveform to move π/2 to the left along the wave direction, so π/2 needs to be subtracted.

Extended data:

Wave equation is a partial differential equation describing wave phenomenon, and its physical meaning is too broad. But a very important property of wave equation is that the propagation speed is limited (unlike heat conduction equation). The motion equation of the electromagnetic field is a wave equation, which shows that the electromagnetic interaction can only propagate at a limited speed (the speed of light C), and there is no instantaneous action (that is, the action at a distance). This is an important idea that led to the establishment of special relativity.

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