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------------------------------------------------ Calculate the pressure amplitude of a 2.00-kHz sound wave in air, assuming that the displacement amplitude is equal to [tex]2.00 \times 10^{-8}[/tex] m.

The pressure amplitude of a sound wave correlates directly with its displacement amplitude. This relationship is given by the formula Ap = sqrt(2pvw), where Ap is the pressure amplitude, p represents air density, and vw signifies the speed of sound in the material. By substituting the provided information into this equation, we are able to calculate the sound wave's pressure amplitude.

Explanation:

To calculate the pressure amplitude of a 2.00-kHz sound wave in air with a displacement amplitude of 2.00 × 10⁻⁸ m, we first need to understand that the amplitude of a sound wave is directly related to its pressure. The relationship between the sound wave's pressure variation, Ap, and its displacement amplitude is given by:

(Ap)² = 2pvw

Here, p represents the air density (1.29 kg/m³ in air at 0°C), vw is the speed of sound in the material (331 m/s in air at 0°C), and Ap is the pressure amplitude.

To find the pressure amplitude, we solve for Ap:

Ap = sqrt(2pvw)

Once we substitute the necessary values into the equation, we can calculate the desired pressure amplitude.

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