Reverberation Time using Sabine Formula (under room temp = 20 degree)
 
RT60 = (0.161 * Room Volume ) / Sa
 
RT60:
Reverberation time to drop 60 dB from direct source sound level
Room Volume:
Room (Width * Length * Height)
 
Sa: Total absorption in sabins
 
Sa = Fc * Floor Area + Cc * Ceiling Area + Wc * Walls * 4
 
Fc: Sound absorption coefficient of Floor material
Cc: Sound absorption coefficient of Ceiling material
Wc: Sound absorption coefficient of Wall material
(The coefficient is the average value between 512 - 1K Hz)
 
Optimum Reverberation Time (based on Stephens and Bate formula)
 
RTop = r [ 0.0118 * Room Volume ^ (1/3) + 0.107)
 
r = 4  :  For Speech
r = 5  :  For Orchestra
r = 6  :  For Choirs
(We use r = 4 for home cinema)
 
SPL Increased by Reverberation
 
SPLr - SPL = 10*log(1 + (4/R)*4Pi*D^2)
R = Sa / (1 - (Sa/S) )
 
SPLr : Sound Pressure Level with 1st reflection
D : Distance between Speaker and Listener
Sa : Total absorption in sabins
S : Sum of Surface
 
(refer to this)

How Your Room Materials Affect The Sound

Have you experienced that your audio systems sound different in your living room than when it was in the audio shop? Don't be surprised. The sound effect is just like the difference you hear someone talking in your empty house and after furniture moved in. Try to add a carpet on the floor, or hang a curtain in front of the concrete wall, which will make your audio systems sound different. 

The experimented graph shown below demonstrates how the room size and material affect the sound pressure level.

The x-axis is the distance from the sound source with directivity factor. The y-axis is the difference between SPL (sound pressure level) and Sound power level. R is the room constant from reverberation coefficient.

In the reverberation field, the SPL is independent of the distance from the source.
The reflection-free line is the one under open space. While the room becomes smaller, more reverberation field will be added to the direct sound source and ends up a relatively flat line. You can also see from the figure that the higher reflection room (lower R), say, with all concrete walls, the larger the reverberation field is and closer to the direct sound, and therefore, the bigger SPL you will hear.

For the SPL increased due to reverberation effect, it will be

SPLrev - SPL = 10*log(1+4/R * 4Pi * r^2)

Source: refer here

Note: the sound absorption coefficient varies with the frequency. Please refer to this for more detail material coefficient with different frequency ranges.

 

Mean Room Sound Absorption Coefficient

 

Mean room sound absorption coefficient = (Total Room Sound Absorption) / (Total Room Surface)

 

Total Room Sound Absorption = Ca * (Surface a) + Cb * (Surface b) + Cc * (Surface c) ….

 

To simplify the calculator, we have calculated 2 side walls, 2 front/back walls, ceiling, and floor. Note that the Room Width, Length, and Height, is the actual room size with walls, but not the area where you put your Hi-Fi Audio.

 

 

Room Effect to Your Sound Pressure Level

 

In the amplifier “Power Calculator” section, we use the distance between your listening position to the speakers, which indicates the “direct” sound pressure level the speakers deliver to you.

In this section, we calculate how the time reverberation sound influences the sound you perceive. Th longer the reverberation time, the fuller or richer the music will sound. Yet too long reverberation times cause the music to sound muddy or even become ‘echoey’ resulting in an inability to hear the music clearly. With short reverberation time the music sounds clear. If too short the music becomes very dry.
Sound reverberation makes you hear louder

Dry Signal

Short Reverberation

Long Reverberation

Source: This article explains the effect of reverberation

 

Sabine formula calculates the reverberation time after the music intensity drops 60 dB to a typical room background sound level.

When under 20-degree Celsius room temperature, the equation can be simplified as below:

Please refer to this for more details on the parameters.

Optimum Reverberation Time

Below shows the optimum reverberation time for different room volume and different purpose based on Stephens and Bate formula.

T60 = K[ 0.0118 Room Volume ^ 1/3 + 0.1070]

Note: We choose K=4 to simulate home cinemas.

Sound reverberation makes you hear louder

 

When a source sound (T1) travels T-direct time to the receiver (T2), it is direct sound, then after reflection, T3 comes the 1st reflection and then the 2nd and 3rd and so on.

If the source sound continues for Tr period of time, the reflection sound starts to add to the direct sound and increase the sound intensity level. (source from here)

Since the 1st reflection impacts the intensity the most, this article calculates the total Sound Pressure Level increased due to 1st reflection, and the increased SPL can be around high for a small room. You may use this Calculator to calculate the increased SPL, then add it (-dB) to your planned SPL and redo your amplifier power calculation. You can refer to below figure on the SPL increased versus room volume size. The lower minus dB, the higher power added. 

Lp: Total Sound Pressure Level

Lw : Sound Power Level

Q : Directive factor

R : Room Constant 

S : Total Surface of the room

Alpha st : Mean reverberation coefficient of the room

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