Question

A change in pressure on the eardrum occurs when a pure musical tone is played. For some
tones, the pressure on the eardrum follows the sine curve
2/14
where is the pressure in pounds per square foot at time t second, and is the frequency of
the sound wave in cycles per second 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 the pressure on the eardrum for Middle C, which has a frequency of / 261.63
H. (ie, cycles per second), for between 0 and 0.005, i.e., [0, 0.005).
(1) Determine the period, denoted by 7 of p(6). What is the relationship between the period
and the frequency of the tone?​

Answer 1

Answer:

  a) see attached

  b) period = 1/f ≈ 3.822 ms

Step-by-step explanation:

Apparently the pressure formula is ...

  $p(t)=0.004\sin{\left(2\pi ft+\dfrac{\pi}{7}\right)}$

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a) A graph of this for f=261.63 is shown in the attachment.

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b) The period is the time T required to change the sine function argument by 2π:

  2πfT = 2π

  T = 1/f  . . . . . .  divide by 2πf

The period is the reciprocal of the frequency.

The period of the tone is 1/(261.63 Hz) ≈ 3.822·10^-3 s