A data buoy measures wave height and transmits the info to a monitoring station. For the minute 11:11 (high tide), wave height can be modeled with the equation y = 3.4 sin ( 2pi/10t) + 3.8 where t is measured in seconds y is in feet. Determine max height of a wave above clam sea and how many waves break during this minute.
I have no idea how to approach this
I have no idea how to approach this
-
Some pointers
The maximum of sin(anything) = 1
So the biggest wave is 3.4*1+3.8.
The sine wave is the height of the waves that oscillates between +3.4 and -3.4 on top of the mean sea level 3.8.
So the biggest wave is 3.4m
The equation of an oscillation, or a wave is sin(2*pi*f*t) where f is the frequency
Alternatively it is sin (2*pi*t/T) where T is the period.
Looking at the equation above, f = 1/10 or T = 10, so the frequency is 0.1Hz and the period is 10sec. The period is the time between successive waves.
If it's 10sec between waves then there are 6 waves in a minute. Or if there's one wave breaking at t=0 then there'll be 7 waves, because the 7th will break when t=60.
The maximum of sin(anything) = 1
So the biggest wave is 3.4*1+3.8.
The sine wave is the height of the waves that oscillates between +3.4 and -3.4 on top of the mean sea level 3.8.
So the biggest wave is 3.4m
The equation of an oscillation, or a wave is sin(2*pi*f*t) where f is the frequency
Alternatively it is sin (2*pi*t/T) where T is the period.
Looking at the equation above, f = 1/10 or T = 10, so the frequency is 0.1Hz and the period is 10sec. The period is the time between successive waves.
If it's 10sec between waves then there are 6 waves in a minute. Or if there's one wave breaking at t=0 then there'll be 7 waves, because the 7th will break when t=60.