Question

If the force on the tympanic membrane (eardrum) increases by about 1.4 N above the force from the atmospheric pressure, the membrane can be damaged. When you go scuba diving in the ocean, below what depth (in feet) could damage to your eardrum start to occur? Considering that your eardrum is 7.4 mm in diameter. Consider the density of sea water to be 1.03*10^3 kg/m^3.

Answer 1

10.58 ft

Step-by-step explanation:

Force, F = 1.4 N

Diameter of membrane = 7.4 mm

radius of membrane, r = 7.4 / 2 = 3.7 mm = 3.7 x 10^-3 m

Area, A = 3.14 x (3.7 x 10^-3)^2 = 4.3 x 10^-5 m^2

Density, d = 1.03 x 10^3 kg/m^3

Pressure at depth, P = h x d x g

Let h be the depth.

Pressure = force / Area

h x 1.03 x 10^3 x 9.8 = 1.4 / (4.3 x 10^-5)

h = 3.225 m = 10.58 ft

Thus, the depth of water is 10.58 ft.