Answer
Damage to the eardrum could start to occur at a depth of 2.8 meters.
Work Step by Step
We can find the pressure on the eardrum that could cause damage.
$P = \frac{F}{A}$
$P = \frac{F}{\pi~r^2}$
$P = \frac{1.5~N}{(\pi)(4.1\times 10^{-3}~m)^2}$
$P = 2.84\times 10^4~N/m^2$
We can find the depth $h$ under the water surface with this gauge pressure.
$\rho~g~h = P$
$h = \frac{P}{\rho~g}$
$h = \frac{2.84\times 10^4~N/m^2}{(1030~kg/m^3)(9.80~m/s^2)}$
$h = 2.8~m$
Damage to the eardrum could start to occur at a depth of 2.8 meters.
