MATH
posted by SC
Danny is measuring the loudness of a police siren. At t=2 seconds, the siren's loudness is at its maximum of 112 dB for the first time. At t=7 seconds, the siren's loudness is at its minimum of 88 dB for the first time. The loudness is a sinusoidal function of time, t. In the first 13 seconds, how much of the time will the loudness be above 94 dB?
So I know the sinusoidal function is this:
y=Asin(2pi/B(xC)+D
A=amplitude=12
D=Mean=100
B=period=???
C=phase shift= xcoordinate of max(B/4)=?????
need help please!

Reiny
your a is correct at 12
your period:
from max to min took 5 seconds, so the whole period is 10 seconds
then 10 = 2pi/k
k = pi/5
so the basic curve could be
y = 12sin(pi/5)(x)
this would have a max of 12 but you want the max to be 112 , so let's move it up 100 units
y = 12sin(pi/5)(x) + 100
Right now our max would be at 2.5 seconds, but we want it to be at 2 seconds, so our graph must be shifted to the left .5 units.
Final curve:
y = 12sin(pi/5)(x + .5) + 100
testing:
if t=2, y = 112 , check!
if t=7, y = 88 check!
now let's set y = 94
94 = 12sin(pi/5)(x + .5) + 100
.5 = sin(pi/5)(x + .5)
(pi/5)(x + .5) = pi+.526599 = 3.66519
x = 5.33333
or
(pi/5)(x + .5) = 2pi.526599 = 5.75959
x = 8.6667
The next set of answers would be 10 seconds later, (the period is 10), but you wanted it only in the first 13 seconds
So between the times of 5.33 and 8.67 seconds we are below 94 decibels, (looking at our graph)
so for a time period of 8.675.33 or 3.34 seconds we are below 94 decibels, which means that in the first 13 seconds, the sound is above
94 decibels for a time of 133.34 seconds or 9.66 seconds
another check:
take a time between the above, say t = 5.5
y = 12sin(pi/5)(5.5 + .5) + 100
= 92.9 which is below 94 
Reiny
got my above and belows mixed up in one line
6th last line should read:
means that in the first 13 seconds, the sound is below
Respond to this Question
Similar Questions

Physics
Initially, you hear the siren at 90 dB. When the distance between you and the ambulance is a quarter of what it was initially, at what intensity level do you hear the siren? 
physical
a police siren emits a sinusoidal wave with frequency f=300hz.the speed of sound is 340ms. find the wave lenght of the waves if the siren is at rest in the air 
8th grade science
The loudness of sound can be measured in decibels. Do you think loudness is a vector or not? 
physical
You are driving along a highway at 27.7 m/s when you hear a siren. You look in the rearview mirror and see a police car approaching you from behind with a constant speed. The frequency of the siren that you hear is 1830. Hz. Right … 
physics
at a distance of 3.8 m from a siren, the sound intensity is 3.6 x 102 W/m2. Assuming that the siren radiates sound uniformly in all directions, find the total power radiated. 
physics
You're in an auto traveling at 25.0m/s toward a pole mounted warning siren. If the siren's frequency is 365 Hz, what frequency do you hear? 
math
The ratio of the loudness of Lana’s earphones to the loudness of Polina’s earphones to the loudness of Goffy’s earphones is 6:5:3. If Polina’s earphones have a loudness of 420 decibels, find the total loudness of all three … 
physics
A marine siren consists of a cylinder 72 cm in length closed at one end.for sound through air at 336 m/s. find the lowest frequency of the siren 
Physics
A siren emits a sound of frequency 1200 kHz. With which frequency is it received by a car moving at a speed of 20 m/s. a) Away from the siren? 
Algebra
The Sound Off Siren Company tests every fifth siren for sound quality and every eighth siren for mechanical quality. The daily output is 360 sirens.What percent is tested for mechanical quality?