$2.(15$ pts$.)$ If the speed of sound in water is $\backslash (1500\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at the surface and increases linearly with depth at a rate of $\backslash (0\mathrm{.}017/\backslash$mathrm$\{$s$\}\backslash ),$ find the range at which a ray emitted horizontally form a source at $100$ m depth will reach surface.

$3.(15$ pts$.)$ For the conditions of the above problem, calculate the ratio of the intensity when the ray reaches the surface to that a $1$ meter from the source. Compare this to the intensity if the spreading were spherical.

$4.(10$ pts$.)$ A Helmholtz resonator has a cylindrical open neck $1$ cm long and $1$ cm in diameter. If the resonating vessel is spherical, what must its radius be to have the resonance frequency be equal to $400$ cps$?$