Tide movement

[itriedit]

I would like some help with the following problem if possible.

I have a sin wave pattern which is showing the tide movement from low to high and back to low(and so on).

The graph shows a 3 meter tidal swing (y axis) and the x axis is time from -6 hours(low water of 0 meters) , high water at 0 hours (3 meters) and back to low water at +6 hours.

The graph is labled hourly interval from nearest high water.


Questions are....
1.
If I rename the graph hourly interval from low water does it make sense that the x axis will now be from 0 to 12 hours in place of the previous -6 to +6 hours.

2.If i am to model this graph I need to place it in the form of y=a sin b(t+c) +d
where y is the tide height and t is the time from since low water.
Now i think that a =1.5 m
and b = pi/6
...but unsure of how do handle the c and d variables.

Any one able to assist please?

 

[tkhunny]

I have a sin wave pattern.
The graph shows a 3 meter tidal swing (y axis).
time from -6 hours(low water of 0 meters) , high water at 0 hours (3 meters) and back to low water at +6 hours.

You have 1.5 m for the amplitude. Good work. a = 1.5 m

A full period is [-6,6], making b = 2*pi/12 = pi/6. Good work.

Phase shift is a bit trickier. You said it was a "sine wave pattern". Does that mean we have to use the "sine" function? If we use the "cosine", which is greatest at x = 0, we're done. Just a hint for the future. Using the sine function, the maximum value, without phase shift, would be at x = (1/4 of a period), or x = 3. We just have to advance it that much. c = 3, as you have it defined. Normally, that would be x-c, and you would get c = -3.

Finally, vertical shift. The sine function, without vertical shift is centered on the x-axis. You just need to jack it up to MINUMUM on x-axis. d = 1.5 m

Changing the x-axis from [-6,6] to [0,12] makes little difference. You get a period from peak to peak, rather than trough to trough. To me, it is of no consequence.

 

[Guest]

Thank you for this - yes I do need to use the sin format in place of the cos option.
So the equation would look like this...

y = 1.5 sin ( (pi/6)(t - 3) ) + 1.5

which is what I also though...now if I was to place this a general equation which works for any tide height (not just 3m), then if the tide height is r and the time to move from low to high tide is f(flood tide time),
then..


y= (r/2) sin ( ( pi/6) (t - (f/2)) ) + (r/2)

Does this look ok?

 

[itriedit]

I posted my next step (used dad's PC and picked his log on up-oops) see apm

can you help some more please.

Thank you for this - yes I do need to use the sin format in place of the cos option.
So the equation would look like this...

y = 1.5 sin ( (pi/6)(t - 3) ) + 1.5

which is what I also though...now if I was to place this a general equation which works for any tide height (not just 3m), then if the tide height is r and the time to move from low to high tide is f(flood tide time),
then..


y= (r/2) sin ( ( pi/6) (t - (f/2)) ) + (r/2)

Does this look ok?