Dispersion relation for air via Kramers-Kronig analysis

Area of Science:

• Acoustics
• Physical Chemistry
• Wave Propagation

Background:

• The International Organization for Standardization (ISO) standard 9613-1 provides a method for calculating the atmospheric attenuation of sound.
• Kramers-Kronig relations are a pair of mathematical formulas that relate the real and imaginary parts of a complex function, often used in physics and engineering.

Discussion:

• This study combines the ISO:9613-1 standard for acoustic attenuation with Kramers-Kronig relations to derive a general expression for acoustic wave dispersion in air.
• The derived expression demonstrates good agreement with existing data for sound velocity across various frequencies and relative humidity levels.
• The research explores how local dispersion characteristics of sound waves are influenced by variations in temperature and humidity.

Key Insights:

• A novel, general expression for acoustic wave dispersion in air has been formulated.
• The model validates well against experimental data for sound velocity under different environmental conditions.
• The study highlights the significant impact of temperature and humidity on sound wave propagation.

Outlook:

• Further refinement of the dispersion model could incorporate a wider range of atmospheric conditions.
• Experimental validation across a broader spectrum of frequencies and humidity levels is recommended.
• The findings could inform more accurate acoustic modeling in diverse environmental and industrial applications.