Propagation Part II: refractionIn general, the sound speed c is determined by a complex relationshipbetween salinity, temperature, and pressure:c = f(S, T, D)Medwin’s formula is a useful approximation for c in seawater:c = 1449.2+4.6T − 0.055T2 + 0.00029T3+(1.34 − 0.010T)(S − 35) + 0.016Dwhere S is the salinity in parts per thousand (ppt), T is the temperature indegrees Celsius, and D is the depth in meters. (See Ogilvie, Appendix A.)Partial derivatives:∂c ∂c ∂c = 4.6 m/sec/C◦ = 1.34 m/sec/ppt = 0.016 m/sec/m ∂T ∂S ∂DFor example:• ∆T = 25◦ =⇒ ∆c = 115 m/sec• ∆S = 5 ppt =⇒ ∆c = 6.5 m/sec• ∆D = 6000 m =⇒ ∆c = 96 m/secsound speedD S Tzccdepth3 PROPAGATION PART II: REFRACTION 21Sound across an interfaceyxθ2θ1θ1k = ω/c 1 1 k = ω/c 2 21ρ , c 1 1 ρ , c 2 2 pppirtp1 = pi + pr = Ie−i(k1x cos θ1+k1y sin θ1) + Re−i(−k1x cos θ1+k1y sin θ1)p2 = pt = T e−i(k2x cos θ2+k2y sin θ2)At x = 0, we require that p1 = p2 (continuity of pressure)(I + R)e−ik1y sin θ1 = T e−ik2y sin θ2Match the phase to get Sne

range with a computer program