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 aluminum (pure) (16650900)brass (36777900)cadmium (24220000)copper (pure) (42018000)gold (61824000)iron (46433000)iron, cast (33152200)lead (22228360)magnesium (10126800)molybdenum (64890000)monel (46926000)nickel (49784000)platinum (70785000)silver (37764000)steel, carbon (46472000)steel, stainless 304 (44660000)tin (24090000)titanium (27694000)tungsten (97864000)uranium (63580000)zinc (30004800)glycerin (2394000)ethanol (2366400)liquid helium (120625)oil, petroleum (1394000)mercury (19017600)water 25°C (1475664)water, sea (1576960)ethanol (2366400)ice (frozen water, 0°C) (3666800)organic glass (plexiglass) (2006000)quartz glass (9860000)hydrogen (106)carbon dioxide (505)dry air (standard conditions, 25°C and 100 kPa) (385)oxygen (452)carbon dioxide (505)aluminium oxide (39303000)nylon (4420000)polyethylene (4370000)rubber, hard (2133000)neoprene (polychloroprene) (1968000)teflon (polytetrafluoroethylene, PTFE) (3080000)fir wood (2200500)pine wood (2618000)neoprene (polychloroprene) (1968000)teflon (polytetrafluoroethylene, PTFE) (3080000)marble (10328910)concrete (9500000)Other - custom parameters Density of substance kilograms per cubic meter [kg/m³]kilograms per cubic decimeter [kg/dm³]kilograms per cubic centimeter [kg/cm³]kilograms per cubic milimeter [kg/mm³]grams per cubic meter [g/m³]grams per cubic decimeter [g/dm³]grams per cubic centimeter [g/cm³]grams per cubic milimeter [g/mm³]miligrams per cubic meter [mg/m³]miligrams per cubic decimeter [mg/dm³]miligrams per cubic centimeter [mg/cm³]miligrams per cubic milimeter [mg/mm³]exograms per liter [Eg/l]teragrams per liter [Tg/l]gigagrams per liter [Gg/l]megagrams per liter [Mg/l]kilograms per liter [kg/l]hektograms per liter [hg/l]dekagrams per liter [dg/l]grams per liter [g/l]decigrams per liter [dg/l]centigrams per liter [cg/l]miligrams per liter [mg/l]micrograms per liter [µg/l]nanograms per liter [ng/l]picograms per liter [ng/l]femtograms per liter [fg/l]attograms per liter [ag/l]pounds per cubic inch [lb/in³]pounds per cubic foot [lb/ft³]pounds per cubic yard [lb/yd³]pounds per gallon (US) [lb/gal (US)]pounds per gallon (UK) [lb/gal (UK)]ounces per cubic inch [oz/in³]ounces per cubic foot [oz/ft³]ounces per gallon (US) [oz/gal (US)]ounces per gallon (UK) [oz/gal (UK)]grains per gallon (US) [gr/gal (US)]grains per gallon (UK) [gr/gal (UK)]grains per cubic foot [gr/ft³]tons (short) per cubic yard [ton (short) / yd³]tons (long) per cubic yard [ton (long) / yd³]slugs per cubic foot [slug/ft³]psis per 1000 foots [psi/1000ft]earth density (mean) [earth density]water density (0 °C, solid) [water (0 °C)]water density (20 °C) [water (20 °C)]water density (4 °C) [water (4 °C)] Sound velocity in the medium kilometres per hour [km/h]kilometres per minute [km/min]kilometres per second [km/s]metres per hour [m/h]metres per minute [m/min]metres per second [m/s]miles per hour [mph]miles per minute [mpm]miles per second [mps]foot per hour [fph]foot per minute [fpm]foot per second [fps]inch per hour [iph]inch per minute [ipm]inch per second [ips]furlong per fortnightspeed of light in vacuum [c]speed of sound in air (20°C, 1 atm)mach [M]knot (nmi/h) [kn] Destination medium Substance name aluminum (pure) (16650900)brass (36777900)cadmium (24220000)copper (pure) (42018000)gold (61824000)iron (46433000)iron, cast (33152200)lead (22228360)magnesium (10126800)molybdenum (64890000)monel (46926000)nickel (49784000)platinum (70785000)silver (37764000)steel, carbon (46472000)steel, stainless 304 (44660000)tin (24090000)titanium (27694000)tungsten (97864000)uranium (63580000)zinc (30004800)glycerin (2394000)ethanol (2366400)liquid helium (120625)oil, petroleum (1394000)mercury (19017600)water 25°C (1475664)water, sea (1576960)ethanol (2366400)ice (frozen water, 0°C) (3666800)organic glass (plexiglass) (2006000)quartz glass (9860000)hydrogen (106)carbon dioxide (505)dry air (standard conditions, 25°C and 100 kPa) (385)oxygen (452)carbon dioxide (505)aluminium oxide (39303000)nylon (4420000)polyethylene (4370000)rubber, hard (2133000)neoprene (polychloroprene) (1968000)teflon (polytetrafluoroethylene, PTFE) (3080000)fir wood (2200500)pine wood (2618000)neoprene (polychloroprene) (1968000)teflon (polytetrafluoroethylene, PTFE) (3080000)marble (10328910)concrete (9500000)Other - custom parameters Density of substance kilograms per cubic meter [kg/m³]kilograms per cubic decimeter [kg/dm³]kilograms per cubic centimeter [kg/cm³]kilograms per cubic milimeter [kg/mm³]grams per cubic meter [g/m³]grams per cubic decimeter [g/dm³]grams per cubic centimeter [g/cm³]grams per cubic milimeter [g/mm³]miligrams per cubic meter [mg/m³]miligrams per cubic decimeter [mg/dm³]miligrams per cubic centimeter [mg/cm³]miligrams per cubic milimeter [mg/mm³]exograms per liter [Eg/l]teragrams per liter [Tg/l]gigagrams per liter [Gg/l]megagrams per liter [Mg/l]kilograms per liter [kg/l]hektograms per liter [hg/l]dekagrams per liter [dg/l]grams per liter [g/l]decigrams per liter [dg/l]centigrams per liter [cg/l]miligrams per liter [mg/l]micrograms per liter [µg/l]nanograms per liter [ng/l]picograms per liter [ng/l]femtograms per liter [fg/l]attograms per liter [ag/l]pounds per cubic inch [lb/in³]pounds per cubic foot [lb/ft³]pounds per cubic yard [lb/yd³]pounds per gallon (US) [lb/gal (US)]pounds per gallon (UK) [lb/gal (UK)]ounces per cubic inch [oz/in³]ounces per cubic foot [oz/ft³]ounces per gallon (US) [oz/gal (US)]ounces per gallon (UK) [oz/gal (UK)]grains per gallon (US) [gr/gal (US)]grains per gallon (UK) [gr/gal (UK)]grains per cubic foot [gr/ft³]tons (short) per cubic yard [ton (short) / yd³]tons (long) per cubic yard [ton (long) / yd³]slugs per cubic foot [slug/ft³]psis per 1000 foots [psi/1000ft]earth density (mean) [earth density]water density (0 °C, solid) [water (0 °C)]water density (20 °C) [water (20 °C)]water density (4 °C) [water (4 °C)] Sound velocity in the medium kilometres per hour [km/h]kilometres per minute [km/min]kilometres per second [km/s]metres per hour [m/h]metres per minute [m/min]metres per second [m/s]miles per hour [mph]miles per minute [mpm]miles per second [mps]foot per hour [fph]foot per minute [fpm]foot per second [fps]inch per hour [iph]inch per minute [ipm]inch per second [ips]furlong per fortnightspeed of light in vacuum [c]speed of sound in air (20°C, 1 atm)mach [M]knot (nmi/h) [kn]

# Results: what is happening at the medium boundary#

 Source medium Density of substance -kg/m³ Sound velocity in the medium -m/s Acoustic impedance 0kg / (m2 s) Destination medium Density of substance 2500kg/m³ Sound velocity in the medium 3800m/s Acoustic impedance 9500000kg / (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 name Reflection coefficient $\beta = \frac{I_1}{I_2}$ Transmission coefficient $\alpha = 1 - \beta$ Transmission coefficient in logarithmic scale [dB]$10~log~\alpha$ aluminum (pure) 1 0 -inf brass 1 0 -inf cadmium 1 0 -inf copper (pure) 1 0 -inf gold 1 0 -inf iron 1 0 -inf iron, cast 1 0 -inf lead 1 0 -inf magnesium 1 0 -inf molybdenum 1 0 -inf monel 1 0 -inf nickel 1 0 -inf platinum 1 0 -inf silver 1 0 -inf steel, carbon 1 0 -inf steel, stainless 304 1 0 -inf tin 1 0 -inf titanium 1 0 -inf tungsten 1 0 -inf uranium 1 0 -inf zinc 1 0 -inf glycerin 1 0 -inf ethanol 1 0 -inf liquid helium 1 0 -inf oil, petroleum 1 0 -inf mercury 1 0 -inf water 25°C 1 0 -inf water, sea 1 0 -inf ethanol 1 0 -inf ice (frozen water, 0°C) 1 0 -inf organic glass (plexiglass) 1 0 -inf quartz glass 1 0 -inf hydrogen 1 0 -inf carbon dioxide 1 0 -inf dry air (standard conditions, 25°C and 100 kPa) 1 0 -inf oxygen 1 0 -inf carbon dioxide 1 0 -inf aluminium oxide 1 0 -inf nylon 1 0 -inf polyethylene 1 0 -inf rubber, hard 1 0 -inf neoprene (polychloroprene) 1 0 -inf teflon (polytetrafluoroethylene, PTFE) 1 0 -inf fir wood 1 0 -inf pine wood 1 0 -inf neoprene (polychloroprene) 1 0 -inf teflon (polytetrafluoroethylene, PTFE) 1 0 -inf marble 1 0 -inf concrete 1 0 -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:
$\beta = \left(\frac{Z_1 - Z_2}{Z_1 + Z_2}\right)^2$
where:
• $\beta$ - intensity reflection coefficient,
• $Z_1$ - acoustic impedance of the first medium,
• $Z_2$ - acoustic impedance of the second medium.
• 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:
$\beta \propto (\Delta Z)^2 \propto (Z_1 - Z_2)^2$
• 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:
$\alpha = 1 - \beta = \frac{4~Z_1~Z_2}{(Z_1 + Z_2)^2}$
where:
• $\alpha$ - intensity transmission coefficient,
• $\beta$ - intensity reflection coefficient,
• $Z_1$ - acoustic impedance of the first medium,
• $Z_2$ - 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).

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