Why do waves travel faster in deeper water?

Hello, I'm an expert in the field of physical oceanography and wave dynamics. Let's dive into the question of why waves travel faster in deeper water. Waves in water are influenced by two main forces: gravity and water depth. In shallow water, the speed of a wave is primarily controlled by gravity. The friction between the wave and the ocean floor causes the wave to slow down. This is because the bottom of the wave is in contact with the sea floor, which creates a drag effect. As a result, the wave's energy is dissipated and its speed is reduced. In deeper water, the situation is different. When a wave moves into deeper water, the water depth is greater than half the wavelength, and the speed of the wave is less affected by the ocean floor. The wave is no longer slowed down by the frictional drag of the sea floor. Instead, the wave's speed is influenced more by its inertia and the water's internal friction. This allows the wave to travel faster because there is less energy loss due to friction. Moreover, in deep water, the wave speed can be described by the following formula: \[ c = \sqrt{\frac{g}{2\pi}} \times T^{1/2} \] where \( c \) is the wave speed, \( g \) is the acceleration due to gravity, and \( T \) is the wave period. This formula shows that the speed of a wave in deep water is dependent on the square root of the wave period, meaning that longer period waves travel faster. In summary, waves travel faster in deeper water because the lack of friction with the ocean floor allows the wave to maintain its energy and speed. The wave's speed in deep water is also influenced by its period, with longer period waves traveling at greater speeds.

Briefly, the deeper the water, the faster a surface wave will travel, and the lower the height will be. As waves come ashore on the ocean, they slow down and get taller, preserving the amount of energy in the wave. The wave speed and variation with depth also depends on the wavelength.