$2.$ Operation Wigwam $\backslash (\{\}^\{1\}\backslash )$ was a test of nuclear device in $1955$ at a depth of $600$ m in the Pacific Ocean $800$ km off the coast of California. The TNT equivalent charge weight of the explosion was $\backslash (30,000,000\backslash$mathrm$\{$~kg$\}\backslash ).$ An unknown number of marine mammals were killed or injured by this explosion including many sea otters on the California coast? Assume that semi$-$ampirical scaling laws discussed in the lectures apply.

a$.$ Estimate the peak pressure at the Califormis coast at a range of $800$ km $?$

$(5$ points$)$

b$.$ What is the time between the detonation and the first bubble pulse?

$(5$ points$)$

c$.$ What is the time constant of the main pressure pulse?

$(5$ points$)$

d$.$ At what range does the pressure pulse maximum amplitude equal ambient pressure at a depth of $600$ meters? Comment on the speed of propagation of the pressure pulse at ranges greater than the range you compute.