### Strutt Help

Coupled Room Decay
**Strutt|Building Acoustics|Coupled Room Decay** Calculates the adjusted reverberation time for coupled rooms. Dumps the energy density decay curves for both rooms.

This user form is based on the formulae in *Principles and Applications of Rooms Acoustics* (see references below).

The user must first complete two RT sheets, one for each room. Make sure to include the coupling surface area in both sheets, with an absorption coefficient of unity across all octave bands .

The user can obtain the 1/1 octave band coupled reverberation time for either room via the userform. In order to plot the energy density decay curves, the user can choose to dump the energy density vs. time data points to a separate new 1/1 octave band sheet. The user can obtain the data points for the energy density decay for either room when teh source rooms has bee nexcited with a steady state signal OR an impulsive signal.

Please note: the reverberation times that the form inputs are calculated using the steady state formula only.

**The Impulsive Excitation Formula**

Room 1 (source room):

`E'_{1}=(P_{1}Deltat)/(V_{1})(e^(-2delta_{1}t)+kappa^{2}(delta_{1}delta_{2})/((delta_{1}-delta_{2})^{2})e^{-2delta_{2}t})`

Room 2 (coupled room):

`E'_{2}=(P_{1}Deltat)/(V_{1})k_{2}(delta_{2}/(delta_{2}-delta_{1}))(e^(-2delta_{1}t)-e^{-2delta_{2}t})`

**The Steady State Excitation Formula**

Room 1 (source room):

`E_{1}\approx(4P_{1})/(cA_{11})(e^(-2delta_{1}t)+kappa^{2}(delta_{1}^{2})/((delta_{2}-delta_{1})^{2})e^{-2delta_{2}t})`

Room 2 (coupled room):

`E_{2}\approx(P_{1})/(cA_{11})k_{2}(delta_{2}/(delta_{2}-delta_{1}))(e^(-2delta_{1}t))-delta_{1}/(delta_{2}-delta_{1})(e^{-2delta_{2}t})`
where:

`E`: energy density of room

`P`: initial sound power

`t`: time

`c`: speed of sound

`A_{11}`: Absorption area of room 1, including coupling area with absorption coefficient of unity

`A_{22}`: Absorption area of room 2, including coupling area with absorption coefficient of unity

`delta_{1}=(cA_{11})/(8V_{1})`

`delta_{2}=(cA_{2})/(8V_{2})`

`V`: Volume of room

`S_{12}`: Surface area of coupling

`k_{1}=S_{12}/A_{11}`

`k_{2}=S_{12}/A_{22}`

`kappa=sqrt(k_{1}k_{2})`

References:

- Cremer, L. & Muller, H.A.,
*Principles and Applications of Room Acoustics*, p261-283

Comments or suggestions to
strutt@arup.com