If the force on the tympanic membrane (eardrum) increases by about 1.50 N above the force from atmospheric pressure, the membrane can be damaged.
When you go scuba diving in the ocean, below what depth could damage to your eardrum start to occur? The eardrum is typically 8.20 mm *.0082m* in diameter. Take the density of seawater to be equal 1.03)10^3 kg/m^3.
To determine the depth at which damage to the eardrum could start to occur while scuba diving in the ocean, we need to understand the pressure exerted on the eardrum at certain depths.
First, let's calculate the pressure exerted by the seawater on the eardrum:
1. Convert the diameter of the eardrum to radius:
Radius = Diameter / 2 = 0.0082 m / 2 = 0.0041 m
2. Calculate the area of the eardrum:
Area = π * Radius^2 = π * (0.0041 m)^2
3. Calculate the force exerted by the seawater:
Force = Pressure * Area
We know that the force on the eardrum should increase by about 1.50 N above the force from atmospheric pressure. Therefore, we can write the equation as:
Pressure * Area = 1.50 N + Pressure_atm * Area
We can simplify this equation to:
Pressure = (1.50 N / Area) + Pressure_atm
Now, let's find the depth at which the pressure reaches the critical level that could damage the eardrum:
1. Convert the density of seawater to SI units:
Density_seawater = 1.03 * 10^3 kg/m^3
2. Calculate the pressure at the critical level:
Pressure_critical = (1.50 N / Area) + (Pressure_atm * Area)
3. Calculate the depth at which this pressure occurs using the hydrostatic pressure equation:
Pressure_critical = Density_seawater * g * Depth
Solving for depth:
Depth = (Pressure_critical / (Density_seawater * g))
Given that the diameter of the eardrum is 8.20 mm (0.0082 m), the density of seawater is 1.03 * 10^3 kg/m^3, and the acceleration due to gravity is approximately 9.8 m/s^2, we can substitute these values into the equation to find the depth:
Depth = (Pressure_critical / (Density_seawater * g))
Depth = ((1.50 N / Area) + (Pressure_atm * Area)) / (Density_seawater * g)
Substituting the appropriate values will give us the depth at which damage to the eardrum could start to occur while scuba diving in the ocean.