Question

The intensity of a certain sound at your eardrum is 0.0040 W/m^ 2 . Calculate the rate P at which sound energy hits your eardrum. Assume that the area of your eardrum is about 51 mm ^2 . P = ______________W What power output P0 is required from a point source that is 1.9 m away in order to create the same intensity at your eardrum? P0 =_____________ W

Answer 1

The rate at which sound energy hits the eardrum can be calculated by multiplying the intensity by the area of the eardrum. The power output required from a point source can be calculated using the inverse square law.

Step-by-step explanation:

To calculate the rate P at which sound energy hits your eardrum, we need to multiply the intensity by the area of the eardrum. P = Intensity x Area.

P = 0.0040 W/m² x (51 mm² / 1000 mm²/m²).

P = 0.000204 W.

To calculate the power output P0 required from a point source that is 1.9 m away to create the same intensity at your eardrum, we need to use the inverse square law. P0 = Intensity x (4πr²), where r is the distance.

P0 = 0.0040 W/m² x (4π x (1.9 m)²).

P0 ≈ 0.182 W.

Answer 2

The rate P at which sound energy hits your eardrum can be calculated by multiplying the intensity by the area of the eardrum. The power output P0 required from a point source to create the same intensity at your eardrum can be calculated using the inverse square law for sound intensity.

Step-by-step explanation:

The rate P at which sound energy hits your eardrum can be calculated by multiplying the intensity by the area of the eardrum. P = intensity × area

Substituting the given values: P = 0.0040 W/m^2 × 51 mm^2 = 0.204 W

To calculate the power output P0 required from a point source that is 1.9 m away to create the same intensity at your eardrum, we need to use the inverse square law for sound intensity.

Intensity follows an inverse square relationship with distance, so P0 = P × (distance_eardrum/distance_source)^2

Substituting the given values: P0 = 0.204 W × (1.9 m / 1 m)^2 = 0.721 W