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Newton's Formula:
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Newton's formula for the speed of sound is an early theoretical approach to calculate the speed of sound in a medium. Although later corrected by Laplace, it represents an important historical milestone in acoustics and fluid dynamics.
The calculator uses Newton's formula:
Where:
Explanation: Newton assumed that sound propagation was an isothermal process, which led to this formula. However, it was later discovered that sound propagation is actually adiabatic, requiring a correction factor.
Details: Understanding the speed of sound is crucial in various fields including acoustics, meteorology, oceanography, and engineering. It helps in designing acoustic systems, studying atmospheric conditions, and developing sonar technology.
Tips: Enter pressure in Pascals (Pa) and density in kilograms per cubic meter (kg/m³). Both values must be positive numbers greater than zero.
Q1: Why was Newton's formula later corrected?
A: Newton assumed isothermal conditions, but sound propagation is actually adiabatic. Laplace corrected it by introducing the adiabatic index (γ), making the formula \( v = \sqrt{\frac{\gamma P}{\rho}} \).
Q2: How accurate is Newton's original formula?
A: Newton's formula underestimates the actual speed of sound by about 15-20% for most gases at standard conditions.
Q3: What is the typical speed of sound in air?
A: At 20°C, the speed of sound in air is approximately 343 m/s using the corrected formula, while Newton's formula gives about 280 m/s.
Q4: Does the formula work for liquids and solids?
A: The basic principle applies, but different materials require different approaches due to variations in compressibility and elastic properties.
Q5: What are the main applications of speed of sound calculations?
A: Applications include acoustic design, ultrasonic testing, medical imaging, atmospheric studies, and underwater communication systems.