Question

A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 10.0 s later. How deep is the ocean at this point? (Note: Use the bulk modulus method to determine the speed of sound in this fluid, rather than using a tabluated value.)
_____ m

Answer 1

the echo time t = 10 s

speed of the water wave v = √K/ρ   ................ (1)

bulkmodulus of the water K = 2*10⁹ N/m²

density of sea water ρ = 1.025*10³ kg/m³

the velocity v = 2d/t   ................... (2)

compare eq (1) and (2) , we get

             2d/t = √K/ρ

dept of the ocean is

           d = (t / 2)√K/ρ

              = (10 s/2)√[(2*10⁹ N/m²)/(1.025*10³ kg/m³)]

              = 6.98*10³ m

             = 6.98 km

              = 7 km (approximately)