International Journal of Advanced Engineering Research and Science (IJAERS) Peer-Reviewed Journal ISSN: 2349-6495(P) | 2456-1908(O) Vol-11, Issue-9; Sep, 2024 Journal Home Page Available: https://ijaers.com/ Article DOI: https://dx.doi.org/10.22161/ijaers.119.1 www.ijaers.com Page | 7 The Relationship Between Wave Period, Deep Water Wave and Breaking Wave Heights, Formulated Using the Wave Amplitude Function Syawaluddin Hutahaean Ocean Engineering Program, Faculty of Civil and Environmental Engineering-Bandung Institute of Technology (ITB), Bandung 40132, Indonesia syawalf1@yahoo.co.id Received: 30 Jul 2024, Receive in revised form: 31 Aug 2024, Accepted: 06 Sep 2024, Available online: 12 Sep 2024 ©2024 The Author(s). Published by AI Publication. This is an open-access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/). Keywords— Wave amplitude function, deep water and breaking wave height. Abstract— The wave amplitude function is a relational equation that links wave amplitude with various water wave parameters, such as wave number, wave angular frequency, and wave constant. This function is derived by integrating the Kinematic Free Surface Boundary Condition over time. The wave amplitude function incorporates breaking characteristics, allowing for the extraction of breaking parameters, including breaking wave height, breaking wave length, and breaking water depth, as functions of the wave period. By combining the Euler momentum conservation equation with the wave amplitude function, a dispersion equation is obtained. This dispersion equation elucidates the relationships between deep water wave height, deep water wave length, and deep water depth in relation to the wave period. The results obtained for both deep water wave height and breaking wave height are consistent with previous research. I. INTRODUCTION Water waves are commonly characterized by two key parameters: wave period and wave height. In the context of short waves, these parameters exhibit a one-to-one correspondence, meaning that a specific wave period is directly associated with a corresponding wave height. This correlation extends not only to deep water wave heights but also to breaking wave heights. In this research, the correlation between deep water wave height and wave period, as well as between breaking wave height and wave period, has been systematically analyzed. The results are presented in the form of equations, tables, and graphical representations. The relationship identified between deep water wave height and wave period aligns with the findings of Wiegel (1949, 1964), while the relationship between breaking wave height and wave period is consistent with the research of Komar and Gaughan (1972). These relationships are valuable for both practical engineering applications and research purposes. Practically, they enable quick estimation of deep water wave height and breaking wave height based solely on the wave period. In the research domain, the ongoing development of water wave transformation models, including processes like shoaling and breaking, necessitates reliable guidelines or estimates regarding the relationship between breaking wave height and wave period. II. WEIGHTED TAYLOR SERIES AND WEIGHTING COEFFICIENT In this article, a specialized equation and parameters are introduced that may not be widely recognized, namely the weighted Taylor series and the associated weighting coefficients.