Graph Showing the Difference Between the Actual Height in Waves and The Models Height in WavesThe graph above highlights the comparison between the height based off of the values found from a graph generated from the equation presented below and the actual high and low tide values found in our general data.
Model GraphThe model graph below shows the theoretical values produced after entering our equation into the Desmos calculator.
Collected DataOn the right is a table organizing all of our data. Although in the in the final production of our graph, not all data was needed. The table shows our calculated time, actual time and model time of the tides as well as the actual and modeled height.
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General DataThe general Data found on the provided website. The time was recorded in the military format here. For the sake of ease in our collected data, the times of the high and low tides were recorded in decimal time format. The military time was converted to decimal time by dividing the minutes by 60 and adding either 48 or 72 to the hours depending on whether the the day recorded was the second or third respectively.
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CalculationsThese are our calculations for the averages and the amplitude. The average high tide was calculated by adding all of the heights of the high tides and dividing them by the six, the number of high tides. The average low tide was calculated by adding all of the heights of the low tides and dividing them by the six, the number of low tides. We then took these values and found the average of them and got 1.253. From there we needed to find the amplitude. We then subtracted the average of averages from the average high tide and thus our amplitude was born!
EquationTo find the cosine equation, we plugged in certain obtained values that we received over the course of our project. For the amplitude, as described above, we subtracted the average of averages from the average high tide. To find the frequency we used the provided value shown on the left. For the horizontal shift we used the decimal time of our first high tide. Finally for the vertical shift, we used the value we obtained from the value of values.
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