Tides go up and down in a 12.8 hour period. The average depth of the river is 9m, and ranges between 7 and 11 m. The variation can be approximated…

Tides go up and down in a 12.8 hour period. The average depth of the river is 9m, and ranges between 7 and 11 m. The variation can be approximated…

Tides go up and down in a 12.8 hour period. The average depth of the river is 9m, and ranges between 7 and 11 m. The variation can be approximated…

This is the equation for a sine curve; y = A sin (B(x-C)) +DY and X are the usual graph axes. We’re letting Y describe the height of the wave (the amplitude) and X describes time. Therefore this sine curve should describe the height of the surface of the water over time.A will represent the amplitude. The amplitude is given by the difference between the average height and the minimum and maximum heights. This value is 2.B will represent the number of complete cycles that the wave goes through over a distance (in time) of 2pi. Since our horizontal axis is time, we need to find out how many 12.8 hour cycles can be completed in 2pi hours. 2pi/12.8 = .49087. So far our equation looks like this: y = 2 sin (.49087(x-C)) +DThis is the equation for a wave with a period of 12.8 hours and a 2-meter amplitude. However, we need to adjust it so that it correctly reflects an average height of 9 meters, and a high point at the 6-hour mark. We will use C and D to adjust the graph along the x and y axes.D is a simple vertical shift of 9.C will represent the horizontal shift. Right now the curve is set 0,9. Since we need to shift to the left (x-C) and sin is involved, we need to do a little more math.We want 11 = 2 sin (.49087(6-C)) + 911 = 2 sin (2.94522 – .49087C) + 9Eliminate the 9, and cancel the 2s.1 = sin (2.94522 – .49087C)arcsin 1 (in radians) = 1.570791.57079 = 2.94522 – .49087C.49087C = 2.94522 – 1.57079.49087C = 1.37443C = 2.8The final equation is y=2sin (.49087(x-2.8))+9Try this out on the link below to see for yourself.