Experiment 2 – Reverberation
EQUIPMENT
Tape measures
Noise making devices (pieces of wood for clappers).
RT app for IOS(Impulso/ClapIR) and Android(AppAcousticRT)
INTRODUCTION
One important application of the study of sound is in the area of acoustics. The acoustic properties of a room
are important for rooms such as lecture halls, auditoriums, libraries and theatres. In this lab we will record and measure
the properties of impulsive sounds in different rooms.
The reverberant sound in an auditorium dies away with time as the sound energy is absorbed by multiple
interactions with the surfaces of the room. In a more reflective room, it will take longer for the sound to die away and the
room is said to be 'live'. In a very absorbent room, the sound will die away quickly and the room will be described as
acoustically 'dead'. The time for reverberation to completely die away will depend upon how loud the sound was to begin
with, and will also depend upon the acuity of the hearing of the observer and the ambient noise level of the room. In
order to provide a reproducible parameter, a standard reverberation time has been defined as the time for the sound to die
away to a level 60 decibels below its original level. The reverberation time, RT60, is the time to drop 60 dB below the
original level of the sound. The reverberation time can be measured using a sharp loud impulsive sound such as a
gunshot, balloon popping or a clap.
Why use 60dB to measure the reverberation time? The reverberation time is perceived as the time for the sound
to die away after the sound source ceases, but that depends upon the intensity of the sound. To have a parameter to
characterize a room that is independent of the intensity of the test sound, it is necessary to define a standard reverberation
time in terms of the drop in intensity from the original level, i.e., to define it in terms of a relative intensity. The choice of
the size of the relative intensity drop to use is arbitrary, but there is a rationale for using 60 dB since the loudest
crescendo for most orchestral music is about 100 dB and a typical room background level for a good music-making area
is about 40 dB. Thus the standard reverberation time is seen to be about the time for the loudest crescendo of the
orchestra to die away to the level of the room background. The 60 dB range is about the range of dynamic levels for
orchestral music.
What is a good reverberation time for a room? If you are using the room for lectures (speech) then a long
reverberation time makes it difficult for the audience to understand words as the echoes interfere. However a long
reverberation time adds character to spaces such as churches where organ music is played. Reflective surfaces lengthen
the reverberation time whereas absorption surfaces shorten it. A larger room usually has a longer reverberation time
because it takes longer for the sound to travel between reflections. Rooms that are good for both speech and music
typically have reverberation times between 1.5 and 2 seconds. The reverberation time is influenced by the absorption
coefficients of the surfaces in a room, but it also depends upon the volume of the room. A small room would not have a
long reverberation time.
An example of a large room with reflective surfaces that has a long reverb time (and so is constantly
unpleasantly noisy) would be Wilson commons. Although it is visually striking this building is atrocious acoustically. It
would be possible to improve the acoustics of this space by hanging artwork made of absorptive materials. The new
biomedical and optics building (Georgen) has a similar problem -- all those beautiful glass surfaces are highly reflective
acoustically (and so you can hear the growl of the espresso machine from the coffee shop everywhere in the building). It
seems that some recently built buildings on campus are designed by architects who have neglected the acoustics of the
spaces. I suspect that it might be possible to compensate for visually striking but acoustically reflective building
materials with cleverly placed acoustic absorbers hidden in the ceilings behind the lights or boldly in the open as 3D
structures on opaque walls.
Predicting the reverberation time and Sabine’s formula.
Sabine is credited with modeling the reverberation time with the simple relationship which is called the Sabine
formula:
(Equation 1)
This formula relates the reverberation time, RT60, to room volume and an effective area. You use the 0.16 sec/m
coefficient if you are working in meters. You use the 0.049 sec/foot coefficient if you are working in ft. Here V is the
volume of the room and Se is an effective area. The effective area is calculated as follows
Here each area Si has an absorption coefficient ai. The effective area is a sum of areas, Si , each with its own
absorption coefficient ai. These areas are the surfaces in the room (ceiling, walls, floor, seats, people, etc…). Another
way to write the effective area is with a sum
Note you must put the areas (Si ) in the same units as the volume V (meter2 for area and meter3 for volume or ft2
for area and ft3 for volume). When a sound wave in a room strikes a surface, a certain fraction of it is absorbed, and a
certain amount is transmitted into the surface. Both of these amounts are lost from the room, and the fractional loss is
characterized by an absorption coefficient, a, which can take values between 0 and 1, 1 being a perfect absorber and 0
being a perfect reflector. Absorption coefficients are unitless. The absorption coefficient is the fraction of the power
absorbed in one reflection. Absorption coefficients for some common materials are given below. The absorption
coefficient of a surface can depend on the frequency of sound used to measure it. For example, carpet is quit absorptive
at high frequencies but not at low frequencies. A perfectly absorptive room would have an effective area that is equal to
the total surface area of its walls, ceiling and floor. A highly reflective room would have an effective area that is smaller
than its total surface area.
The Sabine formula works reasonably well for medium sized auditoriums but is not always an accurate predictor
of the reverb time. The Sabine formula neglects air absorption, which can be significant for large auditoriums. It also
tends to overestimate the reverberation times for enclosures with high absorption coefficients.
Absorption coefficients for common surfaces:
Effective areas for people and seats in auditoriums in sabins
120Hz 250Hz 500Hz 1000Hz 2000Hz 5000Hz
Audience per
person in sabins
0.35 0.43 0.47 0.50 0.55 0.60
Auditorium seat,
solid un- 0.02 0.03 0.03 0.03 0.04 0.04
upholstered
Auditorium seat,
upholstered
0.3 0.3 0.3 0.3 0.35 0.35
A sabin is a unit of acoustic absorption equivalent to the absorption by a square foot of a surface that absorbs all
incident sound.
PURPOSE
The purpose of this lab is to explore the acoustics of different rooms. We can compare the characteristics of
three rooms:
the hallway, a regular size NU Fairview Classroom,and Arch Studio Lab. Your lab group should use two of three of these
rooms to measure sounds. You will measure the reverberation time of one of the rooms using the app and compare your
measured value to those estimated using Sabine’s formula.
PROCEDURE
A. Listening
1. By listening compare the characteristics of the three rooms: Snap your fingers, carry out a conversation, sing,
clap some boards together.
B. Measuring the Reverberation Time
1. Go to one of the two rooms that your lab group has chosen to study.
2. Measure the dimension of the room.
3. Audit and record material finishes of each planar surfaces of the room.
4. Measure and record RT using the recommended app. Record 5 measurement.
5. Record a similar clap in another room and compare the two sound files.
C. Predicting the reverberation time using Sabine’s formula.
1. Using the various measuring devices, estimate the volume of the room.
2. Calculate the surface area of the different absorbing materials in the room.
3. Calculate the affective area of your room, Ae, using absorption coefficients listed above. If a material in your
room is not found on the chart, use google to search the absorption coefficient or NRC of the material.
4. Roughly predict the reverberation time using Reverberation Logarithm formula.
5. Calculate the reverberation time using Sabine’s formula.
D. Measuring Sound Delay and Long Delayed Reflection
1. Draw a scaled section of the room
2. Create a Geometric Ray Diagram showing at least 3 reflected sounds from the sound source and the receiver
3. Use actual measurements.
4. Calculate the time delay of direct sound (d1), and reflected sounds (R1,R2,R3)
5. Does all reflections arrive at listener less than 30millisec
Lab Report Requirements
Your name and collaborators.
An abstract summarizing your major findings.
A plot of decibel vs time showing the rate that sound decays in a room. Your estimate based on this plot for
the reverberation time of that room.
A discussion of whether your reverberation time measured from the plot agreed with what you predicted
using Sabine’s formula.
Reverberation Experiment Worksheet
Name:_________________________________________________date Submitted:________________________
Group name: ___________________________________________
Group Members:
ROOM A:
Draw details floor plan:
Draw Geometric Ray diagram of the room and calculate time delay of reflected sound. Use the space for calculation.
Sound Ray Delay in Ms
D1
R1
R2
R3
R4
Room Data:
Room Name:
Room Dimension
Room Volume
Background Noise
Measured RT (from app) Trial 1 Trial 2 Trial 3 Trial 4 Average RT
Total Room Absorption Value (As)
Calculated RT from Sabine
Formula
Optimum RT from Log Formula
Planar surfaces Material Finishes NRC Value
USE this Space for Calculation
ROOM B: (Room Name)_________________________________
Draw details floor plan:
Draw Geometric Ray diagram of the room and calculate time delay of reflected sound. Use the space for calculation.
Sound Ray Delay in Ms
D1
R1
R2
R3
R4
Room Data:
Room Name:
Room Dimension
Room Volume
Background Noise
Measured RT (from app) Trial 1 Trial 2 Trial 3 Trial 4 Average RT
Total Room Absorption Value (As)
Calculated RT from Sabine
Formula
Optimum RT from Log Formula
Planar surfaces Material Finishes NRC Value
USE this Space for Calculation
Reflection:
1. Does your predicted RT60 agree with the one you measured?
2. discussion of whether your reverberation time measured from the plot agreed with what you predicted using
Sabine’s formula
3. What other effects might account for any difference between your predicted and measured value for the reverberation
time?
