Sinusoids in Nature - Ocean Tides by Chloe Nealon https://padlet.com/chloe_nealon/8e97c9fesruu en-us 2019-03-22 16:14:49 UTC 2024-12-26 01:18:35 UTC hello@padlet.com https://padlet-assets.s3.amazonaws.com/icons/Pictureland.png 1.) In nature, Sinusoidal Functions can be used to measure the tidal change of large bodies of water. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344292726 2019-03-22 16:22:34 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344292726 2.) In order to find the period of the function that determines the tidal changes, one must first find the period of the tidal changes. For example, in Boston, MA, the tide comes in, goes all the way out, and then comes back in again in a period of about 12 hours. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344293448 2019-03-22 16:24:16 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344293448 3.) The period of a typical sine wave is 2π. When we divide 2π by 12 hours, we end up with a new period of π/6. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344295467 2019-03-22 16:28:27 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344295467 4.) A phase shift of 3 is then added to the graph. We do this because the tide changes 3 times in the 12-hour period, thus the graph needs a phase shift to reflect that. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344297048 2019-03-22 16:32:06 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/344297048 5.) To find the amplitude of the function, we have to look at how far the tide will come in and how far the tide will go out. In this case, the tide comes in about 4.8 feet both above and below the midline. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346939560 2019-03-31 19:57:46 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346939560 6.) Finally, we add 5.1 to the end of the graph for a vertical translation. 5.1 is the average height of the tides. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346940491 2019-03-31 20:04:35 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346940491 7.) Here is one period (12-hours of tidal changes) of our graph. As shown below, our midline is 5.1, and there is a total of 3 tide changes in the 12-hour period. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346940981 2019-03-31 20:08:53 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346940981 Here is another example of sinusoids being used to represent ocean tides. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346948148 (Sorry it's sideways) ]]> 2019-03-31 20:53:09 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346948148 Here is the graph for the second example. chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346948647 2019-03-31 20:55:39 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346948647 Citation- chloe_nealon https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346951207 https://www.dummies.com/education/math/trigonometry/measure-tidal-change-using-a-trigonometry-graph/


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]]> 2019-03-31 21:10:53 UTC https://padlet.com/chloe_nealon/8e97c9fesruu/wish/346951207