Final answer:
The enhancement of a seiche to produce a resonance tide necessitates matching the natural frequency of the system with the frequency of incoming waves, leading to resonance and constructive interference, like how a closed-end tube can resonate with a tuning fork.
Step-by-step explanation:
To enhance a seiche and produce a free/forced standing wave, known as a resonance tide, certain period and phase conditions must be met between the tidal constituent (Tc) and the time of perigean spring tides (TPF). Specifically, the natural frequency of the system should align with the driving frequency of the waves. When these frequencies match, or are close to each other, resonance can occur, greatly amplifying the amplitude of the wave, similar to how a closed-end tube can resonate with a tuning fork if the length of the tube allows the reflected sound to arrive back at the source half a cycle later, causing constructive interference. Additionally, for forced standing waves, the occurrence of constructive interference between the incident and reflected waves at free boundary conditions can also enhance the resulting wave amplitude.
In the context of water in a trough with oscillating paddles, the wave function after two waves meet and before they reach the end can be found by combining the individual wave equations using trigonometric identities. When the waves meet, their superposition can lead to constructive interference under the right conditions, potentially resulting in a standing wave if the system's boundaries permit.