The pressures caused by pure tones on the eardrum are sinuso

The pressures caused by pure tones on the eardrum are sinusoidal. The change in pressure P in pounds per square foot on a person\'s eardrum from a pore tone at time t in seconds can be modeled using the equation P = A sin (2 pi ft +phi), where f is the frequency in cycles per second, and phi is the phase angle. When P is positive, there is an increase in pressure and the eardrum is pushed inward; when P is negative, there is a decrease in pressure and the eardrum is pushed outward. A graph of a tone P (t) = .005 sin [2 pi (264.87) t + pi/8]is shown to the right. Complete parts (a) through (c) below. (a) Determine algebraically the values of t for which P = 0 over [0, .005]. The solution set is {}. (Round to five decimal places as needed. Use a comma to separate answers as needed.)

Solution

(a)

P(t)=0.005sin[2(264.87)t +(_/8)]

domain of t is [0,0.005]

0<t<0.005

0*2(264.87)<2(264.87)t<2(264.87)*0.005

0<2(264.87)t<2.64

(_/8)<2(264.87)t+(_/8)<2.64+(_/8)

0.125<2(264.87)t+(_/8)<2.765

Now P(t)=0

0.005sin[2(264.87)t +(_/8)]=0

=>sin[2(264.87)t +(_/8)]=0

=>2(264.87)t +(_/8)= ,2(264.87)t +(_/8)=2

=>2(264.87)t =(7_/8),2(264.87)t =(15_/8)

=>t =(7_/16*264.87),t =(15_/16*264.87)

=>t =0.00165,t=0.00354

the solution set is 0.00165,0.00354