GATE-2018 (24) :Wyllie – Time average equation

 Q. A strong earthquake that occurred in the Indian Ocean settles off a tsunami wave propagating towards Vishakhapatnam. Calculate the velocity of wave (Km/h) and time to reach the Vishakhapatnam coast which is an angular distance of 6 degrees from the epicenter. (Average depth of the Indian Ocean is 4 km).

Solution:

The Velocity (V) of the tsunami is related to the Ocean depth ‘d’ is given by

$V=\sqrt{gd}$

g-acceleration due to gravity =$9.8 m/s^2$

d- Average depth of the Indian Ocean = 4000 m

$V=\sqrt{9.82\times 4000}$

$V=\sqrt{39,240}$

$V=198 m/s$

$V=713 Km/hr$

Time taken for the tsunami to reach the Visakhapatnam Coast is

$time (t)=\frac{Distance}{Velocity}$

$t=\frac{6\times 111}{713}$  

$t=0.934 hr$

 

Extra information:

$1^{0} = 111km$

$6^{0}=6\times 111$

 

Reference : Fundamental of Geophysics, William Lowrie.