Question

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4. Underwater sonar-based monitoring of the seas often involves sending ping-like signals from the sea surface to a receiving, and listening for the reflected signal s]. The sound speed underwater is a function of the static pressure P in [Pa], salinity of the water S in [parts per thousand], latitude Ψ of the location in [deg], temperature T in [deg C], and depth z in [km]. The static pressure is P-99.5(1-0.00263cos 2y)Z+0.239 where z is the depth in [km] and y is the latitude in [deg]. For the oceans, the sound speed is then determined by the relation (4.2) 1449.08+5Tro 1.33(S-35)- (4.2) 0.15225-0) +1.46105- where T is the temperature in [deg C] and S is the salinity in [parts per thousand]. (a) Consider a location with latitudew 40, temperature T-18 [°C], and water salinity S-37 [parts per thousand]. Generate a plot of the sound speed underwater for this location across the depth range of Z-(0, 3] [km. Use a sufficiently large number of points in the plot, which will be beneficial for the effort in (b). Generate this plot of underwater sound speed with positive depth in the downward y axis and sound speed in the x axis like that shown in Figure 3

Answer 1

We are given Static pressure P = 99.5(1 - 0.00263 cos 2i)z + 0.239 z^2 substituting psi = 40 degrees P = 99.5 (+ 0.9995) z + 0.239 z^2 P = 99.5 z + 0.239 z^2 Now we have, C = 1449.08 + 4.57 T e^-[T/869 + (T/360)^2] + 1.33 (s - 35) e^-T/120 + 0.1522 P e^[T/1200 + (s - 35)/400] + 1.46 times 10^-5 P^2 e^-[T/20 + (s - 35) 110] substituting T = 18 degree c s = 37 c = 1449.08 + 4.57(18) e^-[18/26.9 + 1/20^2] + 0.1522 P e[18/1200 + 2/400] + 1.46 times 10^-5 P^2 e^-[18/20 + 1/5] c = 1449.08 + 66.63 + 3.08 + 0.155P + 4.818{2^2} times 10^-6 C = 1519 .51 + 15.42 z + 0.037 z^2 + 0.048 z^2 + 2.75 times 10^-7 z^4 + 0. 000115 z^3 times 2 C = 0.0002 z^3 + 2.75 times 10^-7 z^4 + 0.085z^2 + 15.42 z + 1519.51 \r\n for 0 lessthanorequalto z lessthanorequalto 3 taking z =