# Determination Of Speed Of Sound Using Empirical Equations Biology Essay

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Acoustic sound, navigation and ranging is commonly used for underwater measurement applications. The most popular underwater applications using acoustic sonar is bathymetry surveying, which echo sounder is used to a measured depth. Depths in acoustic sonar are computed based on sonar equation. In sonar equation, elapsed time from a 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 travel time and speed of sound (SOS). If SOS is accurately known, depth can be accurately determined. However, SOS values are subjected to 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 with specific types of water categories (sea water, estuary and fresh water) and compare the value between computed SOS using empirical equations and observed SOS.

Keywords- Speed of Sound (SOS); Acoustic SONAR;Empirical Equations; SVP .

Introduction

In hydrographic surveying, bathymetry is the most popular technique being used in depth measurement. This technique commonly called sounding. Sounding can be carried out using various methods and system such as the mechanical method (Lead line and sounding pole) and acoustic method such as a single beam echo sounder (SBES) and multi beam echo sounder (MBES). Several books explain more details on these methods and systems. [4][5][9][10]

Figure 1. Depth measurement using an acoustic sonar principles

Most of the hydrographic equipments used sonar principle in measuring depth. 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 a transducer to the bottom surface and reflected back are measured. By using following equation depth can easily be computed:

(1)

From the (1), it clearly shows that travel time and speed of sound are the major contributions to determine an accurate depth. Travel time of acoustic sonar can be accurately recorded by 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). Therefore, the speed of sound needs to be determined accurately to ensure accurate computed depth.

Speed of sound in water is variable due to temperature, salinity and density. [1][6]. in the other words, value of speed of sound is not consistent when propagate through different types of water categories. Study of speed of sound is important as most of the sonar equipments are required to set the true value of speed of sound during operations. The aim of this study was to identify the value of speed of sound at various types of water categories (sea water, estuary and fresh water) and finally compare the observed values with resulting values using empirical equations.

Study location

This study was carried out at three different locations based on the aim of the study. For sea water observation, study area was located at Pantai Marang, Terengganu (Fig. 2(a)) as this location is regarded as an open sea and facing to the South China Sea. Taman Tasik Shah Alam, Selangor (Fig. 2 (b)) was chosen as this man-made lake contains of purely fresh water. Kuala Terengganu, Terengganu (Fig. 2 (c)) for estuary observation area was selected due to the mouth of river was expected to have its own tidal prism.

The points marked on the map where the approximate locations for speed of sound observations. The points were located by using a handheld GPS.

Figure 2. Study Area (Google Earth & Google Map)

Field observation and computation

In order to obtain speed of sound at the study area, the flow chart of field observation was constructed and shown at Fig. 3. There were three different selected locations for three types of water categories such as a sea water, fresh water and estuarial site. Firstly, data were collected at sea water at ten different points. The purpose of collecting data at various points was to find the average sound velocity value for each water category. The second data collection was at estuarial site and followed by fresh water. For fresh water, the observation was conducted at two different time zones: night and daytime. These observations were only conducted for fresh water to identify the effect on speed of sound at a different temperatures at the water surface.

Figure 3. Filed Observation Method

Speed of sound data was measured using portable sound velocity profiler (Digibar Pro) developed by ODOM at all proposed locations. The probe was set in time 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 an empirical formula, using Density or Depth (D), Temperature (T) and Salinity (S) data. All these values can be measured or inversely calculated using different types of equipments. In this study, the value of density, temperature, salinity inversely calculated using sound velocity profiler (SVP) equipment. There are 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 velocity are Chin and Millero (1977), Del Grosso (1974), Makenzie (1981) and Medwin (1975) [1]. In this study, speed of sound was estimated based on simple equation (Del Grosso, Mackenzie and Medwin) not a complicated equation (Chin and Millero).

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's equation is simpler compared to Del Grosso equation but still has a restricted in a 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 meters

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 be measured accurately [1].

Speed of sound using svp

Speed of sound at sea water

TABLE 2.VALUE OF 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 speed of sound value directly measured at the sea water depth 0- 6 meters 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 shows that there is no significant increment of speed of sound within the depth of 0-6 meters at sea water. The average value of speed of sound at a seawater site is 1546.1 m/s with respect to the average temperature of 33oC and the average of salinity of 30.2 ppt.

Speed of sound at Estuarial site

TABLE 3. VALUE OF 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 of speed of sound at estuarial site from depth 0-6 meters is 1534 m/s as shown at Table 3. The speed of sound for every depth is based on the average value of 10 different points of observations at the study area. From the results, speed of sound is significantly increased when the water depth and salinity of the water increase. This is the evident to tidal prism occurrences. 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 Table 4, the results show average value of 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 shows that the speed of sound is increased around 0.1-0.5 m/s at the range of depth 0-3.5meters. The average value of speed of sound at fresh water is 1517 m/s with respect to the average temperature of 33oC and the average of salinity of 0.8 ppt.

speed of sound based on empirical equations

Table 5 shows the value of speed of sound at three different empirical equations 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 of 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 equations and direct measurement using SVP at estuarial site. There is no significant difference in terms of speed of sound between calculated using empirical equations and directly measured.

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

TABLE 5: COMPARISON VALUE OF SPEED OF SOUND USING EQUATIONS 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 of speed of sound at sea water, estuarial site and fresh water was discussed 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. It can be concluded that the value of speed of sound for sea water is 1546 m/s, estuarial site is 1534 m/s and fresh water is 1517 m/s. From this study, salinity is the major contribution in the determination of speed of sound at the study area. These findings are valid for the area such as where the observations were made and probably valid for non-extreme climate change countries.