Question
A group of students decided to study the sinusoidal nature of tides. Values for the depth of the water level were recorded at various times. At t=3 hours low tide was recorded at a depth of 1.1 m. At t = 9 hours, high tide was recorded at a depth of 3.7m. Write the equation expressing depth in terms of time.
Answers
Anonymous
mean = ( 1.1+ 3.7 ) / 2 = 2.4
amplitude = (3.7 -1.1)/2 = 1.3
time of mean level tide = (9-3)/2 = 3
tide period T = 2 (9-3) = 12 hours
so
h = 2.4 + 1.3 sin (2 pi (t-3) /12)
amplitude = (3.7 -1.1)/2 = 1.3
time of mean level tide = (9-3)/2 = 3
tide period T = 2 (9-3) = 12 hours
so
h = 2.4 + 1.3 sin (2 pi (t-3) /12)