An audiometer produces a pure tone with a frequency f of 1200 hertz (cycles per second). The maximum pressure P produced from the pure tone is 5 millipascals. Write a sine model that gives the pressure P as a function of the time t (in seconds). Assume P=0 when t=0.

Question

Mathematics

Logan Russell

7 December, 06:10

An audiometer produces a pure tone with a frequency f of 1200 hertz (cycles per second). The maximum pressure P produced from the pure tone is 5 millipascals. Write a sine model that gives the pressure P as a function of the time t (in seconds). Assume P=0 when t=0.

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Answers (1)

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Jayleen Pruitt · Answer 1

Answer: Pressure (t) = 5mP*sin (191.08*t)

Step-by-step explanation:

The information we have:

Maximum pressure P = 5 mP

frequency = 1200Hz

Period = 1/frequency = (1/1200) seconds

when t = 0, P = 0, so we should use a sin function (because sin (0) = 0)

Then we can write this as:

Pressure (t) = P*sin (c*t)

where t is time in secnds, P is the maximum pressure 5mP, and c is a constant that depends on the period.

Pressure (t) = 5*sin (c*t)

knowing that the period is 1/1200 seconds, we have that:

c*1/1200 s = 2*3.14

c = 1200 / (2*3.14) 1/s = 600/3.14 1/s

Our function is

Pressure (t) = 5mP*sin (191.08*t)