The waves you see at the shoreline are actually wind waves and are the sum of many components that were generated by the wind at a distant site. These components travel at different speeds, depending on their period (the time between the arrival of successive crests of these wave components).
For example, the breaker wave you are surfing on, which seems like one wave, is really the combination of many smaller wavelets that happened to arrive at the same time even though they traveled to that location at different speeds. When these wave components come together in very shallow water, the largest one captures the smaller waves and they move at the same speed as the combination starts to break.
While they are in deep water, far offshore, the slowest wave components with the shortest period and the smallest distance between crests could be traveling at less than 5 miles per hour. The components with the longest periods could be moving at more than 35 miles per hour.
These waves will travel thousands of miles until they bump into a shoreline or an island or a reef that makes them break and lose their energy. Waves driven by strong winds around the Antarctic continent, however, can circle that continent forever without encountering land. Fortunately, when they grow to a size that moves as fast as the wind speed, the wind can no longer push them and they will not get any bigger. The Pacific Coast of North America can be impacted by storm waves that originate near New Zealand. These waves can have just the right direction to find a clear path through the islands scattered across the mid-Pacific and find their way to the West Coast mainland.
The speed champions of all the waves are tsunamis. They are usually generated by large rapid movements of the ocean floor caused by earthquakes and aren’t limited by wind speeds. Their speed is limited only by the depth of the ocean along their path. In the center of the Pacific Ocean, their speed can be very close to that of a jet plane, about 600 miles per hour.
-- Richard Seymour, research engineer, Coastal Data Information Program (CDIP)