If you are considering soundproofing measures, you have probably heard that "the heavier the material, the more sound it blocks. This is a basic law of acoustics called the "mass law," which is the most important law when considering transmission loss (sound insulation performance). It is an important concept to understand when implementing soundproofing measures.
However, in actual soundproofing sites, soundproofing performance cannot be explained by mass law transmission loss alone.
This trivia compares theoretical values calculated by the mass law with actual transmission loss data, and explains in an easy-to-understand manner what you need to know to avoid failure in soundproofing measures.
Marketing Group, Corporate Planning Department
Tomoyasu Takaoka
Let's understand the mass law.
The mass law is a law that describes the relationship between the weight of a sound insulation material and its sound insulation performance. In materials composed of a single material, such as concrete or steel plate, the following law holds
- The greater the weight per unit area of material (areal density), the greater the transmission loss (sound insulation performance).
- The higher the frequency, the higher the transmission loss (sound insulation performance).
Here is a brief explanation of the terminology.
Surface density: Weight of material per square meter (kg/m²)
interpoint (interword separation)transmission lossSound Insulation Performance: A numerical value (expressed in dB; the higher the value, the higher the sound insulation performance) that expresses how much sound is reduced when it passes through a wall. The higher the value, the higher the sound insulation performance) ≒ Sound Insulation Performance
Sound Insulation Performance: Ability to block sound
Frequency: Numerical value indicating the height of sound (expressed in Hz. The higher the number, the higher the sound). The higher the number, the higher the sound)
In other words, the rule is that "the heavier the material, the more sound it blocks" and "the higher the sound, the easier it is to block.
Let's calculate transmission loss.
In general, the following equations (1) and (2) are expressed according to the direction of sound incidence.
Vertical incidence (when the sound hits the sound insulation material straight on)
Diffuse incidence (when sound hits the sound insulation material from various directions)
In addition, the following equation (3) is often used at the practical level.
TL0Transmission loss at perpendicular incidence (dB)
TLTransmission loss at turbulent incidence (dB)
mSurface density (kg/m²)
fFrequency (Hz)
Example of calculation of transmission loss by mass law
Table 1 shows the results of the calculation of transmission loss for a typical thickness of steel plate using Equation (3).
Table 1 Transmission loss by mass law (unit: dB)
| 1/1 octave band center frequency (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 |
| Steel plate 1.2 mm, surface density 9.42 kg/m² | 11.3 | 16.7 | 22.1 | 27.5 | 33 | 38.4 |
| Steel plate 2.3 mm, surface density 18.06 kg/m² | 16.4 | 21.8 | 27.2 | 32.6 | 38 | 43.5 |
| Steel plate 3.2 mm, surface density 25.12 kg/m² | 18.9 | 24.4 | 29.8 | 35.2 | 40.6 | 46 |
From equation (3), we find the following
- The heavier the material, the higher the sound insulation performance.
For example, if the weight doubles, the transmission loss (sound insulation performance) increases by approximately 5 dB. - The same material can provide better sound insulation for higher frequency sounds.
For example, if the frequency doubles, the transmission loss (sound insulation performance) increases by approximately 5 dB.
Difference between mass law and actual transmission loss
Comparison of standard performance data and mass law of the Soundproofing Equipment Association (BSK)
So what about actual transmission loss?
Soundproofing Facilities Association (BSK)The following is a comparison of the standard transmission loss of the soundproofing panels and the transmission loss of the mass law for the temporary building of the
The standard transmission loss of BSK's soundproofing panels is a performance standard value determined based on actual measurements by each manufacturer.
BSK-A type soundproofing panel
The values in the mid-band up to 250 Hz are similar to the mass law, but the actual BSK panel has a higher transmission loss in the high frequency band above 500 Hz.
Table 2 Comparison of transmission loss equivalent to 1.2 mm steel plate thickness (theoretical value of mass law and standard transmission loss of BSK-A type soundproofing panel)
| 1/1 octave band center frequency (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 |
| Steel plate t1.2mm Weight rule | 11.3 | 16.7 | 22.1 | 27.5 | 33 | 38.4 |
| BSK-A type soundproofing panel (1.2 mm equivalent) | 13 | 17 | 27 | 35 | 40 | 45 |
| Transmission Loss Difference | 1.7 | 0.3 | 4.9 | 7.5 | 7 | 6.6 |
BSK-B Type Soundproofing Panel
It can be seen that the actual BSK panel transmission loss is above the mass law up to 2000 Hz, and in the 4000 Hz band the panel transmission loss is below.
Table 3 Comparison of transmission loss equivalent to 2.3 mm steel plate thickness (theoretical value of mass law and standard transmission loss of BSK-B type soundproofing panel)
| 1/1 octave band center frequency (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 |
| Steel plate t2.3mm Weight rule | 16.4 | 21.8 | 27.2 | 32.6 | 38 | 43.5 |
| BSK-B type soundproofing panel (2.3 mm equivalent) | 17 | 23 | 33 | 39 | 42 | 38 |
| Transmission Loss Difference | 0.6 | 1.2 | 5.8 | 7.5 | 4 | -5.5 |
BSK-C type soundproofing panel
It can be seen that the transmission loss of the actual BSK panel is above the transmission loss of the panel up to the 500 Hz band, is about the same at 1000 Hz and 2000 Hz, but is below the transmission loss of the panel in the 4000 Hz band.
Table 4 Comparison of transmission loss equivalent to 3.2 mm steel plate thickness (theoretical value of mass law and standard transmission loss of BSK-C type soundproofing panel)
| 1/1 octave band center frequency (Hz) | 125 | 250 | 500 | 1000 | 2000 | 4000 |
| Steel plate t3.2mm Weight rule | 18.9 | 24.4 | 29.8 | 35.2 | 40.6 | 46.0 |
| BSK-C type soundproofing panel (3.2mm equivalent) | 24 | 30 | 37 | 39 | 42 | 40 |
| Transmission Loss Difference | 5.1 | 5.6 | 7.2 | 3.8 | 1.4 | -6.0 |
Impact of the "coincidence effect."
The actual BSK soundproofing panels (2.3 mm and 3.2 mm equivalent) show a significant decrease in transmission loss at high frequencies relative to the mass law values.
This is called the coincidence effect, a phenomenon in which the transmission loss (sound insulation performance) is significantly lower at certain frequencies than at others in a panel composed of a single material. It always occurs and is characterized by the following
- The higher the bending stiffness of the material, the lower the frequency at which it occurs.
- For the same material, the increase in thickness produces at a lower frequency.
From the above, the following characteristics appear in the same iron plate.
- With a thickness of 1.2 mm, the sound insulation performance around 10000 Hz is reduced due to the coincidence effect.
- With a thickness of 2.3 mm, the sound insulation performance around 5000 Hz is reduced due to the coincidence effect.
- With a thickness of 3.2 mm, the sound insulation performance around 3500 Hz is reduced due to the coincidence effect.
The frequency at which the sound insulation performance decreases is called the cohesidence frequency.
BSK's soundproofing panels are thought to have reduced transmission loss in the band around the coincidence frequency due to each thickness affected by these effects.
In other words, BSK-A type panels (1.2 mm equivalent) are not affected by the coincidence effect in the frequency range of 125 Hz to 4000 Hz, and therefore transmission loss is not considered to be reduced, while BSK-C type panels (3.2 mm equivalent) are considered to have reduced transmission loss in the band around the coincidence frequency (4000 Hz The BSK-C type (3.2 mm equivalent) panel is considered to have decreased transmission loss in the band around the coincidence frequency (4000 Hz).
The coincidence frequency of BSK-B type panels (equivalent to 2.3 mm) is 5000 Hz, which affects the 4000 Hz frequency band, but in addition to the 4000 Hz band, the transmission loss in the 2000 Hz band is also reduced. One reason for this may be that some manufacturers in the past used 3.2mm-thick (3500Hz coincidence frequency) steel panels as BSK-B type, and their measured performance data was also reflected in BSK's performance standards.
Also, due to the limited size of actual soundproofing panels, resonance phenomena may occur at low frequencies. This can degrade the performance of the panel. This is one of the reasons why the theoretical value indicated by the mass law differs from the actual performance.
Thus, the mass law approximates the actual transmission loss, but there are many differences. When implementing soundproofing measures, it is important to consider the results of mass law calculations as a guideline for the initial study, and to consider and make decisions based on actual measurement data and test results from third-party organizations.
For those who need help with soundproofing
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