Results of a project during the summer of 2003
| 125 Hz | 250 Hz | 500 Hz | 1000 Hz | 2000 Hz |
| 4000 Hz | Brown Noise | Pink Noise | White Noise | Silence |
Reverberation Time (RT or T60)
For many years I have discussed the concept of reverberation time with my high school physics classes. Although I have played them recordings of similar sounds made in rooms with different reverberation times and showed them a typical decay curves, I have never been able to measure the T60. These activities will allow a group of students to measure the T60 for a room by two methods. The first method is the Sabine method of absorption which involves only the size of the room and the absorbing materials. The second method is actually two similar ways of measuring the sound decay in the room, the Impulse method and the Tone Cut-Off method. Not only can these methods be used by students to calculate the T60 but they can see how well the different methods compare and they can make changes to the room and predict the effect it will have on the T60.
Sabine Method of Absorption
The reverberation time of a room is the time needed for the sound level in the
room to decrease by 60 dB, hence the name T60. Wallace Clement Sabine developed
a method to relate the T60 to the size of the room and the amount and type of
absorbing material in the room.
T60=(0.161s/m)(V)/(S1a1+S2a2+S3a3....)
V - volume of the room in m3.
S - surface area of each of the absorbing surfaces in m2.
a - absorption coefficient for each surface. (see charts)
The product Sa is referred to as the absorption A of a material and is sometimes
expressed in sabins or metric sabins. The sabin is named for professor Sabin
and is equal to the absorption of one square foot of open window. The metric
sabin is equal to one square meter of open window.
In other words a wall with an area of 20m2 and absorption coefficient of 0.3
will absorb as much sound as an open window with an area of 6m2.
Sample Problem
A rectangular room is 10m wide, 15m long and 5m tall. The room has carpet on
concrete with no padding on the floor, painted concrete block walls and a wooden
ceiling. Using the foll
qowing absorption coefficients, find the T60 for the room at 1000Hz.
afloor = 0.37
awalls = 0.07
aceiling = 0.08
Volume = (10m x 15m x 5m) = 750m3
Safloor = (10m x 15m x 0.37 ) = 55.5 m2
Sawalls = (10m +15m) x 5m x 0.07 x 2= 17.5 m2
Saceiling = (10m x 15m x 0.08 ) = 12 m2
SSa = 85 m2
T60 = (0.161s/m)(750m3)/(85 m2) = 1.4 seconds
Absorption Table
This data table was sent to me by Dave Moyer from Riverbank Acoustical Labs.
(See second packet)
Sound Measurements:
Equipment:
Extech Sound Level Meter 407740
LabPro Interface with appropriate cables
Computer or TI Graphing Calculator
Existing Sound System with CD player
Sound Samples on CD*
12" latex balloons
Logger Pro 3.0 software
*In order to make these measurements as simple as possible a CD of tones was
used rather than a signal generator. The intent is that anyone who has the ability
of
down load sound files from a web page and transfer them to a CD will not need
a signal generator. The tones may be down loaded from our web site at the top
of this page.
They include 10 second samples of the following tones.
250Hz
500Hz
1000Hz
2000Hz
4000Hz
Brown Noise
Pink Noise
White Noise
Silence -I found it helpful when using the CD to put a track of silence between
each of the tones.
Impulse method
The impulse method is a quick way of making T60 measurements. It has the advantage
on not needing a frequency generator (CD player). However, the drawback is that
measurements in specific frequency bands cannot be made unless a filter is used
on the receiver. The filter is more likely to be more difficult for the average
high school teacher to get than a CD player. Another problem associated with
the impulse method is that of early reflections. Although these reflections
are an important characteristic of the room and should be observed, their spikes
can make T60 measurements more difficult.
To create a large sound impulse a large balloon is popped in the room while
a sound measurement is made. Not only will a large balloon tend to be louder
than a small balloon but it will also tend to excite more of the lower frequencies.
Tone cut-off method:
The sound absorption coefficient for a material can be different for different
frequencies of sounds. Thus, a material which may be a good absorber of high
frequencies may be a poor absorber of low frequencies. In many applications
only a
certain frequency range is of interest. For example, most speech is in the 500-2000
Hz range. Thus, for a room to deliver speech clearly it would be best to keep
the T60 for these frequencies low.
An acoustic engineer can easily measure the T60 for a specific frequency by
using equipment capable of analyzing different frequencies at the same time.
However, this equipment will cost thousands of dollars. The tone cut off method
is a less expensive but more time consuming way of examining the absorption
of specific frequencies. The procedure is quite simple. A pure tone is played
in the room at a relatively high sound pressure level for a second or two and
then turned off. The sound pressure level vs time graph is then analyzed to
find T60.
Triggers:
Because of the delay between the interface and the computer/calculator, using
a trigger is helpful. I had the least problems
using an increasing trigger with both the impulse method and the cut off method.
During the impulse method the trigger was set, then the sound of the balloon
activated the data collection. During the cut-off method the trigger is set,
then the tone is played. A short time after the trigger has been tripped the
tone is stopped. The trigger, although helpful, is not necessary and quality
data can be obtained without it's use.
Sampling Rates:
The calculator allowed a total of 100 samples. I chose to collect for 4 seconds.
This will be long enough for most rooms of interest. The sampling rate would
then be 25 samples/sec. The computer allowed for much higher sampling rates.
I chose two different rates. 25 samples/sec for 4 seconds to match that of the
calculator and 2500 samples/sec for 4 seconds. The higher value was very near
the highest the hardware/software would allow.
Data Analysis:
I used two similar methods to find T60. Since it is often difficult to measure
a 60dB drop, most acousticians will find T60 by doubling their T30 measurement.
When using the calculator the time for the peak was subtracted from the time
of 30dB less than the peak. This T30 was doubled to find the T60. Since the
time interval between readings was relatively large at 0.04 sec and the sound
level was changing rapidly, the time recorded for the 30dB drop was often an
approximate linear interpolation of the two nearest points to the nearest 0.01
seconds. The second method was to divide 60dB by the slope of the linear regression
line through the decay.
Conclusions:
SLM
The SLM has several settings from which to choose. "A" weighting was
chosen rather than "C" weighting because of the target frequency range.
The 50-100 dB setting was used to best match the sound lev
els. Both the Fast and Slow response settings were tested. In every case the
T60 was lower when the SLM was in the Fast position. Usually the values were
10-20% lower. Since these lower values were more consistent with the results
found by a local acoustic engineer, I suggest the Fast response setting be used
when measuring T60.
25s/s vs 2500 s/s
While using two very different sampling rates, certain trends became clear.
The T60 values were similar. The differences between showed no signs of a consistent
bias. However, it was much easier working with the lower sampling rate. The
data files were much smaller and thus loaded more quickly. The analysis was
faster and easier. At the lower sampling rates the graphs forming in almost
real time made the collection process easier. The main advantage I could see
for the higher sampling rate is the improved definition of shape in the decay
graph.(see graph 1) This is of special interest when studying the resonance
of a room at a particular frequency. I suggest sampling rates between 25s/s
and 2500 s/s but much closer to 25 s/s. I would suggest higher sampling rates
when room resonance is of special interest.
T30 vs Slope
When finding T60 by the two different methods I found that the T30 time gave
a slightly lower value for T60 then by using the slope. This was not true in
every case but an overall result. This is an expected result since the graphs
curve and the range over which the slopes were taken usually extended past the
T30 time.
Clap, Balloon, Tone and Noise
I tried several ways to produce a testable sound. Clapping is the easiest, but
it is difficult to make a clap loud enough except when the clap is very near
the SLM. A large balloon is very good but does not yield information about specific
frequencies. It also introduces detectable reflections which may or may not
be of interest. Pure tones are good for specific frequencies but they may introduce
room resonance which may or may not be of interest*. The Brown, Pink and White
noises were without a doubt the most consistent.(see graphs 2 & 3) The decay
graphs were very linear thus the difference between T30 and slope methods almost
vanished.
*Acoustics labs use rotating deflectors to eliminate resonance within the room.
Room Resonance
I tested three large rooms. A 2500 seat High School Gymnasium and a 600 seat
High School Auditorium both built in the late 60's. I also tested a 300 seat
church sanctuary built in the mid 90's with very little concern for acoustic
properties. The gym and sanctuary both have large parallel walls. The auditorium
had several common acoustical features including sound absorbing material and
few parallel wall surfaces. The gym and Sanctuary both showed a great deal of
room resonance while the auditorium showed almost none.(see graphs 1,3 &
4)
Loudness and Decay
When the tones were played at different sound levels the T60 was slightly different.
In almost every case the louder the sound the shorter the T60. This was to be
expected because of the slight curve of in the graph.(see graph 5)
Room changes
It was quite easy to make changes to the room that would cause measurable changes
in the T60. One of the easiest is to open doors and windows. One obvious problem
with this is that it could allow unwanted sounds to enter. Another simple change
is to add/remove sound absorbing materials. These could be acoustic tile, people,
carpet, pieces of foam, etc.
Background Noise
Background noises are a great concern when doing studies in room acoustics.
These noises often go unnoticed until you start collecting data. It is important
when choosing a room to study to consider when these noises will be at a minimum.
Try to find a time when no other people will be around. Make prior arrangements
for air moving equipment to be turned off. These problems were of special concern
to Wallace Sabine while he was doing studies in Boston during the early 1900's.
So much so that he did many of his studies during the wee hours of the morning.
These were major factors leading him to a new acoustics lab in rural Geneva,
Illinois. History buffs would find the circumstances surrounding his move to
Geneva quite interesting.
Correlation between the different methods
It is somewhat difficult to draw definite conclusions when comparing my results
using the SLM with the results from the acoustical engineer. Although he had
standard professional grade equipment he only collected one sample from three
locations and he only used the impulse method. He also only took measurements
in the church sanctuary. My 500Hz average value is 8% lower than his. The 1000Hz
value is 8% higher. The 2000Hz value is less an 1% lower. Thus, over this frequency
range my average results are very close to the results given by his small sample.
When comparing the measurements taken with the SLM to the Sabine Method of Absorption
the results are not as close. The Sabine method gave T60 times which were 20-50%
lower than the values I measured using the SLM. I attribute this difference
to the uncertainty in the coefficients. The church sanctuary had very large
and uniform surfaces. This made the calculations of the area much easier. However,
since I somewhat unsure of the precise coefficients to use for some of the surfaces,
the T60 values are more uncertain than I would hope them to be.
Future Studies
An area of interest that I did not have time to investigate was the correlation
between the regular "bumps" in the decay graphs and the room dimensions
and location of the SLM. I believe the data I already have might be able to
shed some light on this relationship. The fact that the geometric shape of the
gym and sanctuary are so simple should make the analysis easier.
Final Note
I have found that although the equipment and procedures that were used were
not intended to give the type of results required by acousticians, they are
quite capable of giving the results needed to teach some basic concepts of room
acoustics. The significant advantage is that these results can be obtained with
equipment costing thousands of dollars less than that used by the professionals.
Another advantage is that these procedures could be preformed by a small independent
group of students.
Resources
The Physics Teacher.
Main article: Jesse, K.E. (1980). "A Classroom Acoustical Absorption Experiment,"
TPT 18:41
The Science of Sound Thomas D. Rossing Ph.D
Andrew Morrison NIU Physics Department
Dave Larson S&V Solutions, Inc. Sycamore IL
Dave Moyer Riverbanks Acoustic Laboratories Geneva, IL