Sound wave on medium boundary: reflection and transmission
Calculator finds out sound reflection coefficient between two mediums e.g. air-concrete or steel-steel

Beta version#

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Calculations data: ośrodek źródłowy i docelowy#

Source medium
Substance name
Density of substance
Sound velocity in the medium
Destination medium
Substance name
Density of substance
Sound velocity in the medium

Results: what is happening at the medium boundary#

Source medium
Density of substance-kg/m³
Sound velocity in the medium-m/s
Acoustic impedance0kg / (m2 s)
Destination medium
Density of substance2500kg/m³
Sound velocity in the medium3800m/s
Acoustic impedance9500000kg / (m2 s)
Medium boundary
Reflection coefficient by intensity (β)1
Transmission coefficient by intensity (α)0
Transmission loss in logarithmic scale (10 log α)-infdB

Other target materials#

Values calculated if the target material was the one in the table
Substance nameReflection coefficient β=I1I2\beta = \frac{I_1}{I_2}Transmission coefficient α=1β\alpha = 1 - \betaTransmission coefficient in logarithmic scale [dB]10 log α10~log~\alpha
aluminum (pure)10-inf
copper (pure)10-inf
iron, cast10-inf
steel, carbon10-inf
steel, stainless 30410-inf
liquid helium10-inf
oil, petroleum10-inf
water 25°C10-inf
water, sea10-inf
ice (frozen water, 0°C)10-inf
organic glass (plexiglass)10-inf
quartz glass10-inf
carbon dioxide10-inf
dry air (standard conditions, 25°C and 100 kPa)10-inf
carbon dioxide10-inf
aluminium oxide10-inf
rubber, hard10-inf
neoprene (polychloroprene)10-inf
teflon (polytetrafluoroethylene, PTFE)10-inf
fir wood10-inf
pine wood10-inf
neoprene (polychloroprene)10-inf
teflon (polytetrafluoroethylene, PTFE)10-inf

Some facts#

  • When acoustic wave encounters the medium boundary it may be transmitted to the second medium or it may be reflected (remain in the first medium).
  • How much energy will be transferred between mediums depends on the physical properties of the mediums.
  • For plane wave, which falls perpendicular to the boundary surface, the part of energy that remains in the first medium is determined by reflection coefficient:
    β=(Z1Z2Z1+Z2)2\beta = \left(\frac{Z_1 - Z_2}{Z_1 + Z_2}\right)^2
  • The range of reflection coefficient is from zero to one. Reflection coefficient equal to one (β = 1) means that the wave is reflected completely. The reflection coefficient equal to zero (β = 0) means that the whole energy of the wave is being passed to the second medium (has been absorbed).
  • From the expression for reflection coefficient we can see:
    • the reflection coefficient is directly proportional to the square difference of acoustic impedance of the mediums:
      β(ΔZ)2(Z1Z2)2\beta \propto (\Delta Z)^2 \propto (Z_1 - Z_2)^2
    • the sound barrier (large reflection coefficient) is acoustic impedance difference,
    • because the acoustic impedance depends on the density (to the greatest extent), the greatest insulation is obtained on the gas-solid boundary (e.g. sound from the air is reflected off a wall made of concrete almost completely),
    • the worst insulation can be obtained between mediums of similar impedance e.g. between two metal pipes,
    • acoustic insulation between two solids is more difficult to achieve than between a solid and a gas. The reason is smaller range of available acoustic impedances among solids than between materials with different states of aggregation,
    • in the extreme case when both mediums have identical acoustic impedance (Z1 = Z2) the acoustic wave moves like within one medium.
  • Starting from the law of conservation of energy we can determine the remaining energy that has passed to the second medium. This calculated quantity is usually called transmission coefficient of the medium:
    α=1β=4 Z1 Z2(Z1+Z2)2\alpha = 1 - \beta = \frac{4~Z_1~Z_2}{(Z_1 + Z_2)^2}
    • α\alpha - intensity transmission coefficient,
    • β\beta - intensity reflection coefficient,
    • Z1Z_1 - acoustic impedance of the first medium,
    • Z2Z_2 - acoustic impedance of the second medium.
  • From the expression for the transmission coefficient we can see that sound cannot penetrate into the vacuum (Z2 = 0).

See also#

If you're interested in calculators related to acoustics, check out our other calculators:
  • Sound intensity level (dB) - if you want to learn what is decibel and how the sound intensity level is measured,
  • Sound velocity in materials - if you want to learn how the type of substance affects the speed of acoustic wave propagation,
  • Acoustic impedance of substances - if you want to learn what is acoustic impedance and how it depends on the type of substance,
  • Sound wave reflection - if you want to find out how an acoustic wave behaves when it encounters an obstacle in the form of media boundary,
  • Mass law: single wall - if you're interested in building acoustics and would like to estimate the acoustic insulation of a single wall,
  • Mass law: double wall - if you're interested in building acoustics and would like to estimate the acoustic insulation of a double wall with an air gap between the walls,
  • Sound absorption coefficients - if you're interested in acoustic adaptation of room and you would like to learn how different materials absorb the acoustic wave,
  • Noise propagation - if you want to learn how sound intensity level changes with distance from the source,
  • Sound insulation countours - if you want to learn more about acoustic insulation assessment standards used over the world,
  • Sound reduction index (SRI) - if you're searching for acoustic insulation of popular building materials expressed in the coefficient Rw,
  • Sound transmission class (STC) - if you're searching for acoustic insulation of popular building materials expressed by the index STC.

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