When is the difference between high and low tide the most noticeable?
At what is called spring tides. That is at the new moon and the full moon. Also: twice a month. The reason is: The moon accounts for 70% of the time and the sun for 30%. When they are on the same side or opposite sides, their gravitational pull adds and the tide is higher. The opposite of the spring tide is calle the neap tide. Tides amplitude is not only the result of the pull of the moon and sun, but also how harmonic the water can move. It the to and fro movement is harmonic in the 12 hours between two high tides, then it will be high. This happens e.g. in the Bay of Fundy (the highest tidal difference in the world) and the English Channel.
