Do the following calculations on paper. Scan or photograph and submit. You are building a recording studio, and want to have a high level of sound isolation between the live room and the control room

Laboratory vs. Field Measurements

Because STC is calculated from TL data, the STC of a material or construction can only be determined from a laboratory measurement of TL. However, as with any acoustical parameter, it is important to be able to conduct tests of walls or floor/ceiling constructions in actual buildings for the purpose of verifying performance. For this field testing, we have two descriptors very similar to STC, but specifically designed for testing real construction.

Noise Insulation Class (NIC)

NIC is calculated using the same curve as STC, but the plotted data are measured NR values instead of TL. Last week, you learned that to measure NR, we simply generate broadband noise on one side of a wall, measure the sound pressure levels in the two rooms (in one-third-octave bands), and subtract using the equation above.

In order to overcome the mismatch between NR and TL, a field equivalent to TL can be calculated by simply measuring of A2 and SW for the rooms being tested. A2 is determined by the same method used in the lab—the reverberation time and geometric volume of the room are measured, and the Sabine equation is solved for A. An example of this can be found in lesson 9.

The result of this calculation is not TL, as TL must be measured in the lab. Instead, we call it apparent TL, abbreviated ATL. From one-third-octave ATL values, the ASTC is calculated. The calculation method is identical to that of STC. A direct comparison of STC and ASTC for a wall or floor/ceiling assembly is a useful tool. If the ASTC is significantly lower than the expected STC, it generally means that there is a either a flanking path, or that the wall was improperly constructed. An experienced acoustician will often be able to tell what the specific problem is by comparing the plots of the one-third-octave TL and ATL. Deficiency in the high frequencies, for example, usually indicates flanking.

Composite TL

Up to this point, we have only considered walls that consist of a single construction element. However, in real buildings, we often have walls that have multiple elements, such as a wall with a door or window. When designing such a wall, predicting the TL is not as simple as just looking up a laboratory test, as each of these elements is tested individually in the lab, not as a complete assembly.

The composite TL can be calculated for a particular combination of construction elements (e.g. a wall with a window), using measured TL values for each element and the surface areas occupied by each. To find the composite TL, we must do the following:

1. Convert the TL values for each element (wall, door, window, etc.) to its corresponding transmission coefficient.

2. Calculate the average transmission coefficient of the complete wall, including all elements.

3. Convert the average transmission coefficient back to TL.

Step By Step

Let's look at the math involved for each step.

Step 1: Convert the TL values to 

Last week, you learned that TL and are related as follows:

To convert from TL to , we simply solve this equation for :

We'll look at an example below.

The average transmission coefficient is calculated using this equation:

S represents the surface area of a particular element, and  is its transmission coefficient. We multiply the area of each separate element by its , then add these together to get the numerator. The denominator is simply the total surface area of the wall. We'll look at an example below.

Once we know the value of AVG we convert it to TL using this familiar equation:

Here is a sketch of a wall that is 2.5 m tall and 6 m wide. It contains a window measuring 1 m by 2 m. The main part of the wall is gypsum wallboard (GWB), and has TL of 53 dB, while the TL of the window is only 25 dB. Let's calculate the composite TL using the three steps above:

The values of TL are 53 dB (GWB) and 25 dB (window).

GWB:

Remember that  is a ratio, so it is unitless.

To calculate AVG we need to know the surface area and  of each element. We calculated the values of  in step 1. The surface areas are:

Window: (1 m)(2 m) = 2 m2

GWB: (2.5 m)(6 m) - 2 m2 = 13 m2

Note that the area of the window was subtracted from overall area of the wall.

The total area of the wall is (2.5 m)(6 m) = 15 m2

We then put these values into the equation and solve:

The AVG is 4.26×10-4.

The composite TL for this wall assembly is 33.7 dB.

Remember that all of this is very frequency dependent, which means that these calculations have to be done separately for each octave or one-third-octave band. This is a lot of work, and is typically done with a spreadsheet on a computer.