The Bay of Fundy

Date: 04/13/97 at 17:23:14
From: Nikita Bacchus
Subject: Bay of Fundy
 
Hi Dr. Math,

The Bay of Fundy in Canada is reputed to have the largest tides in 
the world, with the difference between low and high water level being 
as much as 15 meters.  Suppose  at a particular point in the Bay of 
Fundy, the dept of the water, y meters, as a function of time, t, in 
hours since midnight on Jan 1, 1994, is given by

   y=y0+Acos[B(t-t0)]

What is the physical meaning of y0?
What is the value of A?
What is the value of B?  

Assume the time between successive high tides is 12.5 hours.
What is the physical meaning of t0?

Date: 04/14/97 at 10:20:03
From: Doctor Anthony
Subject: Re: Bay of Fundy

y0 is the water depth halfway between low and high water.
A is the amplitude of the cos curve = 7.5 metres

To find B we require that when t - t0 = 12.5 hours we are back to same 
value.  So if B = 2.pi/12.5 = pi/6.25 this will make the cos curve 
repeat itself every 12.5 hours.  We put B = pi/6.25 = 0.50265.

The physical meaning of t0.  When t = t0 we have y = y0 + A which is 
high water, and so t0 is the time of last high water.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/