# The principle of mass does not serve as the basis for calculating sound insulation

07/02/2024

To achieve soundproofing, heavy materials must be used.

This is often said, but it is based on the principle of mass. However, relying solely on the principle of mass to calculate sound insulation can be risky.

## Mass Principle

The principle that the transmission loss ( sound insulation ) increases as the mass per unit area of a wall increases is known as the mass law. This is recognized as fundamental knowledge about sound.

From this, the idea that using heavy materials is necessary for soundproofing is based on the mass law. However, the mass law alone does not serve as the basis for calculating the required sound insulation.

We would explain the reasons for this. ( Note: In this article, we will exclude things like hollow double walls or composite panels and focus solely on the mass law.)

## The mass law is merely a rough guideline

It is incorrect to apply the mass law to all cases of noise mitigation, but is often used as the basis for calculating the required sound insulation .

TL＝18log(f×M)̶44

TL：Transmission Loss（㏈）

f：Frequency（Hz）

M：Mass per unit area（㎏/per square meter）

According to this calculation, with soundproofing materials weighing 40 kg/m², the transmission loss would be 20 dB at 250 Hz. Therefore, if I build a soundproof room with dimensions of 2 meters (height) × 2 meters (width) × 2.5 meters (height) using the material weighing 40 kg/m², the sound insulation should be 28 dB @ 250 Hz. → No, It won’t be.

So, is the mass law a lie ? → No, it is not a lie.

## The truth behind the Mass Law

The mass law is based on specific measured values of the transmission loss of the material in question (hereinafter referred to as the subject).

In this case, sound pressure is measured as energy per square meter (1 m²). When calculating transmission sound using the mass law, it is converted per square meter.

In other words, the mass law does not apply to objects larger or smaller than 1 square meter.

“The soundproof room in the example, with dimensions 2m (height) × 2m (width) × 2.5m (height), has a surface area of over 24 square meters, so it falls outside the scope of the mass law and therefore, in most cases, the mass law does not apply.”

When the object in question exceeds 1 square meter or is smaller than 1 square meter, how does the transmission loss change ?

### WHEN THE SURFACE AREA EXCEEDS 1 SQUARE METER (WITH THE SAME MATERIAL AND STRUCTURE )

The transmission loss tends to decrease in the low to mid-frequency range. Errors can occur in the high-frequency domain.

### WHEN THE SURFACE AREA IS SMALLER THAN 1 SQUARE METER (WITH THE SAME MATERIAL AND STRUCTURE )

The transmission loss tends to increase across the entire frequency range.

Simply put, the trend is that transmission loss decreases as the surface area increases, and transmission loss increases as the surface area decreases. One reason for this is the effect of vibration on the object. As the object becomes larger, it tends to vibrate more easily.

Sound propagates through air or through the vibration of objects. When an object vibrates easily, it can become a secondary source of vibration itself. This can lead to additional losses such as frictional losses. Conversely, increasing the difficulty of vibration ( increasing impedance ) of the object tends to increase transmission loss ( whether transmission loss is the appropriate term in this context is uncertain).

In essence, increasing mass generally correlates with increased resistance to vibration, hence the notion that “ using heavy materials is necessary for soundproofing” is not entirely wrong. However, for smaller objects, the difficulty in vibration also increases, which means the mass law may not accurately predict transmission loss in such cases.

The larger the object becomes, the more important it is to increase its mass. The mass law focuses on individual materials rather than considering the overall context.