Respuesta :
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)
For the audiometer tone, the sine model which gives the pressure value as a function of time is,
[tex]p(t)=5\sin(191t)\rm mP[/tex]
What is audiometer?
The audiometer is the device which produces the pure tone to test the audibility to hear sound.
For the sound wave, the sine model for the pressure in terms of time can be given as,
[tex]p(t)=P\sin(ct)[/tex]
Here, (t) is the time, P is the maximum pressure and c is the constant.
An audiometer produces a pure tone with a frequency f of 1200 hertz (cycles per second).
To find the value of sine mode, we need to know the time period of it. As, the time period is inverse of the frequency of the wave and the frequency is 1200 Hz. Therefore,
[tex]T=\dfrac{1}{1200}\\[/tex]
The value of constant can be found out as,
[tex]c=\dfrac{T}{2\pi}\\c=\dfrac{1200}{2\times \pi}\\c\cong191[/tex]
The maximum pressure P produced from the pure tone is 5 millipascals. Put the values in the above model function as,
[tex]p(t)=5\sin(191t)\rm mP[/tex]
Hence, For the audiometer tone, the sine model which gives the pressure value as a function of time is,
[tex]p(t)=5\sin(191t)\rm mP[/tex]
Learn more about the audiometer here;
https://brainly.com/question/9999708
