# Speed Of Sound Using Empirical Equations Biology Essay

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Acoustic sound, navigation and ranging are commonly used for underwater measurement applications. The most popular underwater applications using acoustic sonar is bathymetry surveying which echo sounder is to measured depth. Depths in acoustic sonar are computed based on sonar equation. In sonar equation, elapsed time from sensor transmitting sonar wave to the bottom and reflected back to the sensor were measured. The main parameter contributing in computation of depth using acoustic sonar are travels time and speed of sound (SOS). If SOS accurately known, depth can accurately determine. The values of SOS are various depend on the temperature, salinity and density. There are various equipments and formula can be used to determine SOS accurately. This paper will discuss on field observation of SOS value at different types of water (sea water, estuary and fresh water) and compare the of SOS computed using empirical equations and SVP data

In field of hydrography, Bathymetry is most popular technique used in depth measurement. This technique commonly called sounding. Sounding can be carried out using various method and system such as mechanical method (Lead line and sounding pole) and acoustic method (single beam echo sounder (SBES) and multi beam echo sounder (MBES)). Several book explain more detail on these method and system. [4][5][9][10]

Figure 1: Depth measurement using acoustic sonar principle

Most of hydrographic instrument or system used sonar principle in measuring depth. The Fig. 1 shows the basic principle of depth measurement using acoustic sonar.

In depth determination using acoustic sonar, travel time of acoustic sonar transmitted from transducer to the bottom surface and reflected back are measured. By using following equation depth can easily computed:

(1)

From the equation (1), it clearly shown that to travel time and speed of sound is the major contribution to determine accurate depth. Travel time of acoustic sonar can be accurately measured using echo sounder however speed of sound may be measured accurately using direct (Velocity profiler or Conductivity, Temperature and Depth sensor) or indirect method (bar check and empirical formula). It means that the speed of sound need to determine accurately to make sure computed depth is accurate.

Speed of sound in water is variable due and depends on the temperature, salinity and density. [1][6]. in the other words, value speed of sound not consistent when propagate through different types of water. Study of speed of sound are need cause of most of sonar equipments need to setting and alter the speed of sound value. The aim of this study was to identify the value of speed of sound at the various types of water (sea water, estuary and fresh water) and finally compare the value with empirical equations.

study area

This study was carried out at 3 different locations based on the aim of the the study. For sea water observation, study area is located at Pantai Marang, Terengganu (Fig. 2(a)), Taman Tasik Shah Alam, Selangor (Fig. 2 (b)) for fresh water observation and Kuala Terengganu, Terengganu (Fig. 2 (c)) for estuary observation area.

The point marked on the on the map are the approximate location whereby each point are the location of the speed of sound observation was conducted. The points are located by using a handheld GPS.

Figure 2 Study Area

Field observation and computation

In order to obtain speed of sound at the study area, the flow chart of field observation are constructed and shown at Fig. 3. There are three different location were selected for the three types of water that is sea water, fresh water and estuarial site. Firstly data are collected at sea water at ten different points. The purpose of collecting data at various points is to find the average sound velocity data for each type of water followed by sound velocity at estuarial site and fresh water. For fresh water, the observation was conducted at two different times that is at night and day time. These observations are only conducted at the fresh water to identify the effect of speed of sound at different temperature at the surface of water.

Figure 3 Filed Observation Method

Speed of sound data were measured using portable sound velocity profiler (Digibar Pro) developed by ODOM at all proposed location. The probe was set in times data acquisition mode and lowered the probe from the surface layer to the bottom layer (Fig 4.)

Figure 4 Steps in lowering probe

The value of speed of sound can be determined by using empirical formula, by using the Density or Depth (D), Temperature (T) and Salinity (S). All this value can be measured or inversely calculated using several different types of instruments. In this study, the value of density, temperature, salinity inversely calculated using sound velocity profiler (SVP) equipment. There is several numbers of equations available to calculate the speed of sound in water from the less accurate (simples equation) to the most accurate (complicated equations). The most popular and accurate equation for calculating sound of velocity are Chin and Millero (1977), Del Grosso (1974), Makenzie (1981) and Medwin (1975) [1]. In this study, speed of sound is estimated based on simple equation not a complicated equation (Del Grosso, Mackenzie and Medwin).

Del Grosso (1974) equation.

Del Grosso equation has a more restricted range of validity. Range of validity for temperature is from 0 to 30 Â°C, salinity 30 to 40 parts per thousand, pressure 0 to 1000 kg/cm2. This equation used as an alternative to UNESCO algorithm. Following equation already reformulated for new 1990 International Temperature Scale [12] and their version is:

c(S,T,P) = C000 +âˆ†CT +âˆ†CS +âˆ†CP +âˆ†CSTP (2)

where,

âˆ†CT(T) = CT1T + CT2T2 + CT3T3

âˆ†CS(S) = CS1S + CS2S2

âˆ†CP(P) = CP1P + CP2P2 + CP3P3

âˆ†CSTP(S,T,P) = CTPTP + CT3PT3P + CTP2TP2 + CT2P2T2P2 + CTP3TP3 +CSTST + CST2ST2 + CSTPSTP + CS2TPS2TP + CS2P2S2P2

* T = temperature in degrees Celsius, S = salinity in Practical Salinity Units, P = pressure in kg/cm2

The coefficients value of the Del Grosso equations are shown in table 1.

Table 1: Coefficients in the Del Grosso equation for calculating speed of sound

Coefficients

Numerical values

C000

1402.392

CT1

5.01E+00

CT2

-5.51E-02

CT3

2.22E-04

CS1

1.33E+00

CS2

1.29E-04

CP1

0.1560592

CP2

2.45E-05

CP3

-8.83E-09

CST

-1.28E-02

CTP

6.35E-03

CT2P2

2.66E-08

CTP2

-1.59E-06

CTP3

5.22E-10

CT3P

-4.38E-07

CS2P2

-1.62E-09

CST2

9.69E-05

CS2TP

4.86E-06

CSTP

-3.41E-04

Mackenzie (1981) equation.

Mackenzie equation is more simple compared to Del Grosso equation but still has a restricted in range of validity. This equation used a function of temperature, salinity and depth. The different between Mackenzie, Chen & Millero and Del Grosso is uses of depth in the equation. Range of validity for temperature is from 2 to 30 Â°C, salinity 25 to 40 parts per thousand, depth 0 to 8000m.

c(D,S,T) = 1448.96 + 4.591T - 5.304 x 10-2T2 +

2.374 x 10-4T3 + 1.340 (S-35) + (3)

1.630 x 10-2D + 1.675 x 10-7D2 -

10-2T(S - 35) - 7.139 x 10-13TD3

*T = temperature in degrees Celsius, S = salinity in parts per thousand, D = depth in metres

Medwin (1975) equation.

This equation is the simplest equation in computing speed of sound. Medwin equation is given as:

c = 1449.2 + 4.6T âˆ’ 0.055T 2 + 0.00029 T 3 +

(1.34 âˆ’ 0.010T)(S âˆ’ 35) + 0.016 D (4)

*T = temperature in degrees Celsius, S = salinity in parts per thousand, D = depth in metres

This equation is valid for realistic combinations of Temperature, Salinity and Depth. The range of validity of Medwin equation in the ranges, temperature 0 to 35 Â°C, salinity 0 to 40 parts per thousand and depth 0 to 1000 m. By using this equation all the parameters must measured accurately [1].

Speed of sound using svp

Speed of sound at sea water

Table 2: Value speed of sound at sea water using sound velocity profiler equipment

## DEPTH

## SOS

## SALINITY

## TEMP

## Â

## (m/s)

## (ppt)

## (OC)

0

1546

30.7

33

0.5

1546

30.6

33

1

1546.1

30.3

33

1.5

1546.1

30.2

33

2

1546.1

30.2

33

2.5

1546.1

30.3

33

3

1546.1

30.3

33

3.5

1546.1

30.3

33

4

1546.1

30.2

33

4.5

1546.1

30

33

5

1546.1

29.8

33

5.5

1546.2

29.9

33

6

1546.2

30.1

33

## AVERAGE

## 1546.1

## 30.2

## 33

Table 2 shows the results of average value speed of sound directly measured at the sea water depth 0- 6 meter using sound velocity profiler. The speed of sound every depth shown at the table 2 is based on the average value of 10 different points of observations at the study area. The result shown that the value speed of sound is not having significant increased from depth 0-6 meters at sea water. The average value speed of sound at estuarial site is 1546.1 m/s with respect the average temperature of 33oC and the average of salinity of 30.2 ppt.

Speed of sound at Estuarial site

Table 3: Value speed of sound at Estuarial Site using sound velocity profiler equipment

## DEPTH

## SOS

## SALINITY

## TEMP

## Â

## (m/s)

## (ppt)

## (OC)

0

1523.1

13.4

30

0.5

1523.4

13.7

30

1

1525.1

15.4

30

1.5

1526.9

17.7

30

2

1531.6

21.6

30

2.5

1533.9

24.2

30

3

1536.5

26.4

30

3.5

1537.7

27.8

30

4

1539.6

29.7

30

4.5

1540

29.6

30

5

1541

30.3

30

5.5

1541.3

30.9

30

6

1541.5

30.9

30

## AVERAGE

## 1534

## 24.0

## 30

The average value speed of sound at estuarial site from depth 0-6 meters is 1534 m/s as shown at table 3. The speed of sound every depth is based on the average value of 10 different points of observations at the study area. From the result, value speed of sound shown significantly increases when the water depth and salinity of water increase. However the value of temperature is remaining constant at 30oC at all depth.

Speed of sound at fresh water

Table 4: Value of speed of sound at fresh water using sound velocity profiler equipment

## DEPTH

## SOS

## SALINITY

## TEMP

## Â

## (m/s)

## (ppt)

## (OC)

0

1515.7

0

33

0.5

1515.7

0

33

1

1516.2

0

33

1.5

1516.5

0.2

33

2

1516.8

0.7

33

2.5

1517.3

1.7

33

3

1517.9

1.8

33

3.5

1518

1.8

33

## AVERAGE

## 1517

## 0.8

## 33

In the table 4, the results shows average value speed of sound directly measured at the fresh water for depth at range 0-3.5 meters. The speed of sound every depth is based on the average value of 7 different points at day and night observations. From the result, it shown that the value speed of sound is increased around 0.1-0.5 m/s at range of depth 0-3.5meters. The average value of speed of sound at fresh water is 1517 m/s with respect the average temperature of 33oC and the average of salinity of 0.8 ppt.

speed of sound based empirical equation

Table 5 shows the value of speed of sound at three different empirical equation and differences with the value directly collected using SVP at sea water, estuarial site and fresh water. From this table 5(a), the difference value speed of sound calculated using empirical equation and value from SVP at the range 0.2-0.5 m/s at sea water. Del Grosso equations showed the highest differences meanwhile Medwin equation showed the lowest difference at sea water.

Table 5(b) shows, the differences value of speed of sound calculated using empirical equation and direct measurement using SVP at estuarial site. The value speed of sound has shown constant between calculated using empirical equations and directly measured.

At the fresh water, value speed of sound using Del Grosso equation and value from SVP has same value of 1516.7 m/s. However, by using Medwin and Mackenzie equation, the value of differences between calculated and direct measurement is at range 0.1-0.3m/s as shown at table 5(c).

Table 5: Comparison value of speed of sound using equation and SVP at (a) Sea water (b) Estuarial site (c) Fresh water

(a)

## EQUATION

## SOS

## SOS (SVP)

## DIFF

## Â

## (m/s)

(m/s)

(m/s)

Del Grosso

1546.6

1546.1

0.5

Mackenzie

1546.5

1546.1

0.4

Medwin

1546.3

1546.1

0.2

(b)

## EQUATION

## SOS

## SOS (SVP)

## DIFF

## Â

## (m/s)

(m/s)

(m/s)

Del Grosso

1534.1

1534

0.1

Mackenzie

1534.1

1534

0.1

Medwin

1534.2

1534

0.2

(c)

## EQUATION

## SOS

## SOS (SVP)

## DIFF

## Â

## (m/s)

(m/s)

(m/s)

Del Grosso

1516.7

1516.7

0

Mackenzie

1517

1516.7

0.3

Medwin

1516.6

1516.7

0.1

Conclusion

Value speed of sound at sea water, estuarial site and fresh water was discuss and presented in this paper. These results of study give useful information for preliminary stage for sounding purposes. With this value, hydrographer will save time in selecting suitable speed of sound in calibrating echo sounder equipment. The result showed the value speed of sound at sea water is 1546.1m/s, estuarial site is 1534 m/s and fresh water is 1517 m/s. From this study, salinity is major contribution in determination of speed of sound at the study area.