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Newton's Isothermal Formula:
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Newton's isothermal formula calculates the speed of sound in a medium based on pressure and density. It assumes an isothermal process where temperature remains constant during sound propagation.
The calculator uses Newton's formula:
Where:
Explanation: The formula derives from Newton's assumption that sound propagation is an isothermal process, relating the speed of sound directly to the square root of the ratio of pressure to density.
Details: Calculating the speed of sound is essential in various fields including acoustics, meteorology, oceanography, and engineering. It helps in understanding wave propagation, designing acoustic systems, and studying atmospheric conditions.
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 is Newton's formula considered isothermal?
A: Newton assumed that during sound propagation, the temperature remains constant (isothermal process), which later was corrected by Laplace who considered adiabatic conditions.
Q2: How accurate is Newton's formula compared to modern formulas?
A: Newton's formula underestimates the actual speed of sound because it doesn't account for adiabatic compression and expansion. The Laplace correction provides more accurate results.
Q3: In which media does Newton's formula apply?
A: The formula applies to gases where the assumptions of isothermal processes might be considered, though it's primarily of historical significance today.
Q4: What are typical values for speed of sound?
A: In dry air at 20°C, the speed of sound is approximately 343 m/s. In water, it's about 1480 m/s, and in steel, it can reach 5100 m/s.
Q5: Why is density important in sound speed calculation?
A: Density affects how quickly sound waves can propagate through a medium. Denser materials generally transmit sound faster due to closer molecular spacing.