Calculating Frequency, Energy & Power of Sound Waves

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The discussion centers on the relationship between sound wave properties and their effects on the human tympanum. The equation F = 4x describes the force acting on the tympanum based on its displacement. A sound wave with a frequency of 1000 Hz causes a displacement of 1.5 x 10^-5 m, leading to calculations for energy transfer and average power. The intensity of the wave is defined as the power per unit area, with a specific formula that incorporates wave speed, medium density, frequency, and amplitude. Understanding these relationships is crucial for analyzing how sound waves interact with biological systems.
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The human tympanum is displaced by sound waves. This displacement is linked to the acting force by the equation:

F = 4x

where x is the displacement in meters.

A wave of frequency 1000 Hz provoques a displacement of 1.5 x 10^-5 m. Prove that the energy given to the tympanum is given in 0.25*10^-3 s. Also find the average power of the wave.

I don't how power is linked to frequency and energy in therms of waves...
 
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The intensity of a wave is defined as
I=\frac{P}{S}
where P is its power (the amount of energy it transports per second) through a (perpendicular) cross sectional area S.

The intensity is given by
I=2\pi^2v\rho f^2A^2
which includes the propagation speed of the wave, v, while it is traveling throught a medium of density \rho, creating a disturbance with a frequency f and amplitude A.
 
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