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Velocity of Sound in the Sea
Storyboard 
The speed of sound in the sea depends on the pressure, temperature and salinity.
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Speed of sound with depth
Concept
The speed of sound in the ocean varies with depth as shown in the graph:
The shape of the curve can vary depending on the time of year.
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Dependence on the speed of sound
Concept
The speed of sound in the ocean depends on the temperature and pressure as shown in the graph:
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Model
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Parameters
Variables
Calculations
to 
, then, select the variable: 
to 
Calculations
Calculations
Variable 
Given Calculate 
Target : Equation To be used 
Equations
$ c = c_0 T ^3- c_1 T ^2+( c_3 - c_2 s ) T + c_4 p + c_5 s - c_6 $
c = c_0 * T ^3- c_1 * T ^2+( c_3 - c_2 * s )* T + c_4 * p +c_5 * s - c_6
$\displaystyle\frac{ \sin\theta_i }{\sin \theta_r }=\displaystyle\frac{ c_i }{ c_e }$
sin( theta_i )/sin( theta_r )= c_i / c_e
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Ley de Snell en función de la velocidad
Equation
La relación entre los ángulos de incidencia y refractados indicados en la siguiente gráfica
se pueden escribir en función de la velocidad de la luz en cada medio
| $\displaystyle\frac{ \sin\theta_i }{\sin \theta_r }=\displaystyle\frac{ c_i }{ c_e }$ |
Observando la imagen se nota que los senos de los angulos son respectivamente\\n\\n
$\sin\theta_i=\displaystyle\frac{c_i\Delta t}{d}$
y\\n\\n
$\sin\theta_e=\displaystyle\frac{c_e\Delta t}{d}$
\\n\\nSi se despeja en ambas ecuaciones la distancia
$d=\displaystyle\frac{c_i\Delta t}{\sin\theta_i}=\displaystyle\frac{c_e\Delta t}{\sin\theta_e}$
por lo que se tiene que
| $\displaystyle\frac{ \sin\theta_i }{\sin \theta_r }=\displaystyle\frac{ c_i }{ c_e }$ |
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Sound velocity equation
Equation
In 1977, Clay and Medwin developed a model to estimate the speed of sound based on temperature, salinity, and pressure.
the speed of sound ($c$) can be estimated based on the presión hidrostatica ($p$), the temperature ($T$), and the salinity ($s$) using the following expression:
| $ c = c_0 T ^3- c_1 T ^2+( c_3 - c_2 s ) T + c_4 p + c_5 s - c_6 $ |
where $c_i$ are empirical constants.
Reference: "Study of Absorption loss effects on acoustic wave propagation in shallow water using different empirical Models", Yasin Yousif Al-Aboosi, Mustafa Sami Ahmed, Nor Shahida Mohd Shah, and Nor Hisham Haji Khamis, ARPN Journal of Engineering and Applied Sciences, Vol. 12, No. 22, November 2017.
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