Final Answer:
The amplitude of 3 Pascals and the frequency of 330 hertz in the sine model P(t) = 3sin(330t) align with the given tuning fork's characteristics, making it the accurate representation. Options C and D are eliminated due to incorrect frequencies and the introduction of a cosine function.The correct sine model that gives the pressure P as a function of time is P(t) = 3sin(330t).So the correct option is A) P(t)= 3sin(330t).
Step-by-step explanation:
The general form of a sine function is given by P(t) = A * sin(Bt), where A is the amplitude and B is the frequency. In this case, the amplitude is given as 3 Pascals, and the frequency is 330 hertz. Therefore, the correct sine model is P(t) = 3sin(330t).
Here, the amplitude represents the maximum pressure produced by the tuning fork, which is 3 Pascals. The frequency, 330 hertz, corresponds to the number of cycles per second. The argument of the sine function, 330t, ensures that the pressure varies sinusoidally with time.
Option C, P(t) = 3sin(990t), can be ruled out because it suggests a frequency of 990 hertz, which is not consistent with the given information. Similarly, option D, P(t) = 3cos(990t), introduces a cosine function, and the correct model is based on a sine function. Therefore, option A, P(t) = 3sin(330t), accurately represents the pressure as a function of time for the given tuning fork.
In summary, the correct sine model for the pressure P as a function of time is P(t) = 3sin(330t), reflecting the amplitude and frequency characteristics of the tuning fork's vibrations.So the correct option is A) P(t)= 3sin(330t).