What type of tide occurs during the quarter moon phases?
The exceptionally low high tides (and high low tides) that occur
during the quarter-moon phase are known as "neap tides."
Conversely, the exceptionally high and low tides that occur during
full and new moons are known as "spring tides."
Strictly speaking, however, although there is a correlation
between moon phase and tidal activity, this is not truly due to the
moon. Tides are caused by the moon's orbit around the earth; the
moon's gravity pulls a swell of water on the the side of the earth
facing it, and a corresponding bulge on the opposite side. These
vary several times per day, with the moon's once-daily orbit of the
earth. So, there are about 12 hours between high tides.
Moon phases, on the other hand are purely a visual phenomenon,
varying based on the the viewing angle of the moon from our vantage
point, here on earth, relative to the sun. When the sun is shining
behind the moon, we observe a new moon. On the front side? A full
moon. When the earth, moon, and sun are aligned at roughly a 90
degree angle? A half moon. And, of course there's every phase in
between. During any given day during the cycle, the tides continue
to rise and fall independent of what lunar phase we happen to
observe.
The spring and neap tides are actually caused by the sun. Like
the moon, the sun also exerts a gravitational pull on the side of
the earth that faces it, causing high tides every twelve hours --
solar tides; Although this effect is far weaker than the lunar
tides (about half the effect), the height of the tide at any given
time is a composite of the gravitational vectors of the sun and
moon, added together, like constructive or destructive
interference. Thus, when the sun and moon are on the same side of
the earth (or opposite sides), their collective gravity works
together and magnifies the effect, and tides are higher and lower
than usual; this is what occurs during new moons and full moons --
the spring tides. Alternately, when the sun and moon are located at
90 degrees with respect to the earth, the sun and moon pull along
different axes, and cancel each other out to some degree; this is
what occurs during quarter moons, when tides vary far less than at
other times of the month... not so high and not so low.
There is also a proxigean spring tide, an extremely high tide
that occurs very rarely when the moon's orbital eccentricity also
magnifies these gravitational tidal effects. This occurs when the
moon's lowest point of orbit (proxigee) coincides with a full or
new moon (already very high tides).
Incidentally, lunar phases are not caused by the earth's shadow
falling on the moon. This would be an eclipse, which is quite
rare.