A simplified formula for the speed of sound in water is C=1449+4.6T-0.055T 2 +1.

Question

A simplified formula for the speed of sound in water is

C=1449+4.6T-0.055T2 +1.4(S-35)+0.017D(m/s)

where T is temperature (degress celsius), S is salinity and D is depth in meters. Suppose an experiment is set up to measure the mean ocean temperature with a sound source and reciever located 5,000 km apart. Assume the sound path follows a mean depth of 1000m, where the mean salinity is 35 psu.

If the travel time between source and reciever (1-way) is 56 minutes and 28.25 seconds, what is the mean temperature of the water?

(knowing distance can infer the temperature)

Explanation / Answer

C = 1449+ 4.6T -0.055T^2 +1.4(S-35)+0.017D(m/s) '

speed = 1449 + 4.6 T - 0.055T^2 + 1.4 * ( 35 - 35 ) + 0.017 * 1000 ;

distance /t = 1449 + 4.6 T - 0.055T^2 + 1.4 * ( 35 - 35 ) + 0.017 * 1000 ;

or ( 5000e3 ) / ( 56 * 60 + 28.25 ) = 1449 + 4.6 T - 0.055T^2 + 1.4 * ( 35 - 35 ) + 0.017 * 1000 ;   

or 1475.688 = 1449 + 4.6 T - 0.055T^2 + 1.4 * ( 35 - 35 ) + 0.017 * 1000 ;   

solving this ,

or T = 2.1619 C , or T = 81.474 degree C ;

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