Mechanical Properties of Fluids

Question

Compressional wave impulses are sent to the bottom of sea from the ship and the echo is heard after 1.8s. Find the depth of sea. Assume that the density of sea water is 1000kg/m³ and bulk modulus of water is 2.25x10⁹ N/m².

Solution

Given,
$Density comma space straight rho equals 1000 space k g divided by straight m cubed comma E n e r g y comma space straight E space equals space 2.25 cross times 10 to the power of 9 space straight N divided by straight m squared$
Therefore velocity of sound in sea water,
$straight v equals square root of straight E over straight rho end root equals square root of fraction numerator 2.25 cross times 10 to the power of 9 over denominator 1000 end fraction end root equals 1500 space straight m divided by straight s$
Let d be the depth of the sea.
As the echo is heard after 1.8s, therefore the wave travels 2d distance in water in time 1.8s.
i.e. $2 straight d equals vt$
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