I am trying to find a summed sine wave for my assignment that fits the data points of tide readings from a specific coastal region (Avalon Beach).
The requirements are as follows:
- both tides must touch their averages
- Major (first): 1.82, 0.245
- Minor (second): 1.6175, 0.2725
- peaks should align with data points on the x-axis
- equation should be [math]asin(bx+c)+dsin(ex+f)+g[/math] where 2b ≈ e and d>a
The data points, average lines and other info is at https://www.desmos.com/calculator/ahlz9vqimg
I remember doing a bit of summed sine waves before, but not at this level, only adding 2 equations to get an answer, and not the other way around. I'm not sure what a summed sine wave "model" is.
Things I previously tried:
- Making 1 uniform sine wave that hits the x-axis of the points and the average of the averages of the y-axis of the points (was told to make complex graph)
- Adding 2 sine waves that were zeroed where the other wave was meant to be shown (increasing height centre of 1 increased the height centre of the total)
- Adding 2 sine waves that were "Noned" (i.e. no value/line) where the other value was meant to be shown (cut-off graphs, was told to sum sine waves instead)
I am stuck with the summing because the graph moves in an unusual way, where moving 'c' or 'f' separate from each other changes the height, and I am unsure of how to change the height centre since it's different for both tides.
The requirements are as follows:
- both tides must touch their averages
- Major (first): 1.82, 0.245
- Minor (second): 1.6175, 0.2725
- peaks should align with data points on the x-axis
- equation should be [math]asin(bx+c)+dsin(ex+f)+g[/math] where 2b ≈ e and d>a
The data points, average lines and other info is at https://www.desmos.com/calculator/ahlz9vqimg
I remember doing a bit of summed sine waves before, but not at this level, only adding 2 equations to get an answer, and not the other way around. I'm not sure what a summed sine wave "model" is.
Things I previously tried:
- Making 1 uniform sine wave that hits the x-axis of the points and the average of the averages of the y-axis of the points (was told to make complex graph)
- Adding 2 sine waves that were zeroed where the other wave was meant to be shown (increasing height centre of 1 increased the height centre of the total)
- Adding 2 sine waves that were "Noned" (i.e. no value/line) where the other value was meant to be shown (cut-off graphs, was told to sum sine waves instead)
I am stuck with the summing because the graph moves in an unusual way, where moving 'c' or 'f' separate from each other changes the height, and I am unsure of how to change the height centre since it's different for both tides.