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Ohh you mean **moon** phases, yes I'm well aware of how and why the moon phases effect tide.
That one is very easy to explain thankfully and we dont need to get into all that advanced stuff to do it.
It is simple really. The pull of the sun and the moon both effect tides. In both cases it will cause a very strong tide ont he side closest to the moon/sun, a weaker high tide on the far side, and low tides on either side.
I attached an illustration so you can see.
This effect occurs simultaneously between the moon and the sun, with the moon having a stronger influence than the sun.
Therefore the effects are either add together or cancel. You can imagine that when the moon and the sun are in a straight line the effect adds up as the gravity of each are in line with each other. However if the moon is at a 90 degree angle then they will cancel out and give weaker tides.
Since the moon always lines up at full or new moon, and is always at 90 degree angles at a waning or waxing half moon, it is clear to see why the phase of the moon would directly effect the magnitude of the tides.
Hope that clears up your misconceptions for you.
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