The sound velocity in water can be calculated using specific formulas that account for factors like temperature, pressure, and salinity. Based on the provided reference, for a specific temperature range in water, a simplified formula can be used.
The Formula for Sound Velocity in Water (Temperature Dependent)
According to the reference, a simple and accurate formula for sound velocity in water, particularly useful within a specific temperature range, is:
c = 1404.3 + 4.7 T - 0.04 T²
Where:
- c is the sound velocity in meters per second (m s⁻¹)
- T is the temperature in degrees Celsius (°C)
This formula is designed to provide values accurate within 0.20 m s⁻¹ over the temperature range of 15°C to 35°C.
How to Use the Formula
To calculate the sound velocity using this formula, you only need the water's temperature (T) within the valid range (15°C to 35°C).
- Measure the temperature of the water in degrees Celsius (°C).
- Substitute the measured temperature (T) into the formula.
- Calculate the result to get the sound velocity (c) in meters per second (m s⁻¹).
Example Calculation
Let's calculate the sound velocity in water at a temperature of 25°C using the formula:
- Identify the temperature: T = 25°C
- Substitute into the formula:
c = 1404.3 + 4.7 (25) - 0.04 (25)² - Perform the calculation:
c = 1404.3 + (4.7 25) - (0.04 625)
c = 1404.3 + 117.5 - 25
c = 1519.3 - 25
c = 1494.3 m s⁻¹
So, according to this formula, the sound velocity in water at 25°C is approximately 1494.3 m s⁻¹.
Important Considerations
- This specific formula is valid only for the temperature range of 15°C to 35°C. For temperatures outside this range, or when pressure and salinity are significant factors (e.g., in deep ocean water or saltwater), more complex formulas are required.
- The formula is designed for use in water, typically fresh or standard seawater conditions within the specified constraints.
- The stated accuracy of this formula is within 0.20 m s⁻¹ within its valid temperature range, making it suitable for applications where this level of precision is acceptable.
Understanding the conditions under which a specific formula is derived and valid is crucial for accurate calculations of sound velocity in water.
