Sound travels differently through various materials, influenced by their properties and environmental conditions. This section explores how factors like temperature, density, and composition affect sound speed in gases, liquids, and solids.

We'll dive into equations for calculating sound speed and compare speeds across different media. Understanding these concepts helps explain everyday phenomena like sound refraction in the atmosphere and underwater acoustics.

Factors Influencing Sound Speed

Medium Properties and Temperature Effects

• Speed of sound primarily influenced by elastic properties and density of the medium
• Temperature alters kinetic energy of particles in gases and liquids
  • Changes medium's elasticity
  • Affects sound speed more significantly in gases and liquids than solids
• Density inversely influences sound speed
  • Higher density generally decreases sound speed (assuming other factors constant)
• Humidity changes average molecular mass of air
  • Affects sound speed in atmosphere
• Pressure minimally affects sound speed in gases under normal conditions
  • Becomes significant at extreme pressures (deep ocean, planetary atmospheres)

Material-Specific Influences

• Solid materials' sound speed determined by elastic modulus and density
  • Temperature has less significant effect compared to gases and liquids
• Metals typically have higher sound speeds than non-metallic solids
  • Due to higher elastic moduli and lower compressibility
• Composition changes alter sound speed
  • Salinity in water (ocean vs freshwater)
  • Alloying in metals (steel vs pure iron)

Calculating Sound Speed

General Equations

• Speed of sound in any medium: $v = \sqrt{B/ρ}$
  • v: speed of sound
  • B: bulk modulus
  • ρ: density of medium
• Ideal gases: $v = \sqrt{γRT/M}$
  • γ: adiabatic index
  • R: universal gas constant
  • T: absolute temperature
  • M: molar mass of gas

Medium-Specific Calculations

• Liquids: $v = \sqrt{K/ρ}$
  • K: bulk modulus of liquid
• Solids (longitudinal waves): $v = \sqrt{Y/ρ}$
  • Y: Young's modulus
• Solids (transverse waves): $v = \sqrt{G/ρ}$
  • G: shear modulus
• Temperature-dependent equations for specific media
  • Used for accurate calculations in varying environmental conditions (air at different altitudes)

Sound Speed: Materials vs Conditions

Comparative Sound Speeds

• Sound travels fastest in solids, then liquids, then gases
  • Due to differences in particle proximity and bond strength
• Speed of sound in water ~4.3 times faster than air at room temperature
• Air at 20°C: ~343 m/s
• Steel: can exceed 5000 m/s
• Demonstrates vast difference between gases, liquids, and solids

Environmental Factors

• Gases: sound speed increases with temperature
  • Independent of pressure under normal conditions
• Composition affects sound speed
  • Salinity increases sound speed in water (ocean vs lakes)
  • Alloying elements change sound speed in metals (steel vs aluminum)
• Pressure becomes significant at extreme conditions
  • Deep ocean: increased pressure raises sound speed
  • Upper atmosphere: low pressure decreases sound speed

Medium Properties and Sound Propagation

Wave Behavior in Changing Media

• Temperature gradients in atmosphere cause sound wave refraction
  • Creates phenomena like sound shadows (areas of reduced sound intensity)
  • Forms sound channels (layers where sound travels long distances)
• Acoustic impedance mismatches at medium boundaries
  • Causes partial reflection and transmission of sound waves
  • Affects sound propagation between different layers (air-water interface)
• Frequency-dependent sound absorption
  • Alters propagation of complex sounds
  • Changes timbre over distance (high frequencies attenuate faster)

Complex Propagation Effects

• Inhomogeneities scatter sound waves
  • Suspended particles or bubbles in liquids
  • Creates acoustic shadows behind obstacles
• Boundaries guide wave propagation
  • Walls in buildings create reverberations
  • Ocean floor and surface form underwater sound channels
• External factors change medium's elastic properties
  • Stress alters sound speed in solids (pre-stressed concrete)
  • Temperature variations affect sound propagation in atmosphere (creating inversions)