A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate
objects under water. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine?
(Speed of sound in water = 1450 m s ^–1).

Solution

Let the distance between the ship and the enemy submarine be ‘S’.

Speed space of space sound space in space water space equals space 1450 space straight m divided by straight s space Time space lag space between space transmssion space and reception space of space Sonar space waves space equals space 77 space straight s In space this space time space lag comma space sound space waves space travel space straight a space distance space which space is space twice space the space distance space between space the space ship space and space the space submarine space left parenthesis 2 straight S right parenthesis. Time space taken space for space the space sound space to space reach space the space submarine space equals space 1 divided by 2 space cross times space 77 space equals space 38.5 space straight s space Therefore comma space Distance space between space the space ship space and space the space submarine comma space left parenthesis straight S right parenthesis space equals space 1450 space cross times space 38.5 space space space space space space space equals space 55825 space straight m space equals space 55.8 space km

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