# PHYS

NEED TO BE FINISHED BEFORE THE END OF TODAY

Category: Engineering & Sciences Subjects: Electrical Engineering Deadline: 12 Hours Budget: \$120 - \$180 Pages: 2-3 Pages (Short Assignment)

## Attachment 1

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Last/First Name (print):

Experiment 5:

Reverberation Time

Pre-lab (10 Points)

1. If a room has an absorption of Se = 13 sabines, and the volume of the room is 300 meters cubed, what is the reverberation time in this room?

2. Reverberation time is defined as the time it takes for a sound intensity to drop by dB. (fill in the blank)

3. Inside a room, if a sound wave hits a wall with an open door, the door acts as a: (circle one)

perfect absorber

perfect reflector

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4. If a closed door of dimensions 3 m x 1.5 m has an absorption coefficient of 0.5, what is the door's contribution, in sabins, to the total absorption of the room when the door is closed?

5. Referring to the previous question, what is the door's contribution if it is left open?

Last/First Name (print): PHYS -Section Username ID (xxx9999):

PRE-Lab Summary (15 points)

Read the experiment before coming to lab.

1) Summarize the procedure for this experiment on the page below. 2) Include the purpose, procedure and calculations that you will need. 3) This summary should be in your own words in bullet format. You may

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= 1 d

Last/First Name (print):

Experiment 5:

Reverberation Time

1 Background

1.1 Reverberation

Reverberation is the sustained sound that exists in an enclosed space after the source of the sound is turned off. It is caused by the combined effects of multiple sound reflections within the space. As an ever increasing number of reflections combine at the point of measurement, the sound becomes “smooth” or continuous, and only a gradual decay of the sound intensity is perceived. Individual reflections or echoes are not heard.

1.2 Reverberant Sound

Imagine the sounds that you hear if a single short percussive note is played in an enclosed space. This sound could be a single snare drum strike or a pistol shot, for example.

The shortest distance between the sound source and your ears is the straight line between the source and your head. The direct sound travels along this line and is the first sound that you hear. Other sounds travel to your ears after first being reflected from one of the walls, the ceiling or the floor. The sounds which arrive within 50 to 100 msec after the direct sound are called the early reflections. As time goes on, you hear more and more reflections that have bounced off more and more walls. Each reflection becomes weaker than its predecessor because the energy continuously spreads out as described by the inverse square law:

I2 I1

d 2 2 2

(1)

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The I’s represent the sound intensity levels and the d’s represent the distance from the sound source. The sound intensity level (SIL) at any new location is inversely proportional to the square of the increase in the distance. For example, if the distance is doubled, the SIL decreases by 2 × 2 = 4, so the new intensity is one–fourth of the original intensity. This is a lowering of the SIL by 6 dB.

The sound reflections which arrive later merge together and are perceived as a continuously decaying sound, called the reverberant sound.

1.3 Reverberation Time

The reverberation time Tr of a room is defined as the time is takes the sound level to drop 60 dB below its original level. This is more than sufficient for most humans to judge that the sound has disappeared. Scientifically, it is the time required for the amplitude to decrease to 1/1000 of its original level, or for the intensity to decrease to one–millionth of its original level.

1.4 Human Perception of Reverberation Time

If a series of notes or words are presented to humans, the reverberation of the preceding note or word is usually not noticed after its SIL drops 10 to 15 dB below the note currently being played. Therefore, if a room has a 2 sec reverberation time, only the notes which occur within about a half second of each other overlap (15 dB x 4 = 60 dB).

To hear the reverberation of a room clearly, a loud sound must be followed by complete silence. Humans usually underestimate the reverberation time and are likely to choose 30 to 40 dB decays instead of the 60 dB in the definition of reverberation time. However, with training and practice, the 60 dB reverberation time can be estimated very accurately (to within 0.1 sec!).

1.5 Reverberation Time Measurement

Reverberation time is measured by allowing the SIL in a room to equilibrate into a smooth sound. The sound is then abruptly terminated. For best results, narrow band white noise is used to avoid particularly live or dead frequencies that might exist in a room. Alternatively, a very loud, short transient sound impulse may be used.

The SIL is monitored as a function of time and plotted on a graph similar to that shown in Figure 1a. A line is drawn or calculated for the best linear fit through the decay of the sound. The reverberation time is the time required for a 60 dB decrease in the SIL, even if the SIL cannot be measured over this range due to background noise or other effects.

Poorly designed rooms may have nonlinear decay curves such as those shown in Figures 1b and 1c. Decay curves of this sort are indications that the reverberation will not be pleasing to hear, or that there are strong natural modes in the frequency range used for the measurement.

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Figure 1. Examples of Reverberation Time Measurements that Could Occur in

Well-designed (a) and Poorly Designed (b and c) Rooms

1.6 Optimal Reverberation Times

Optimal reverberation times are dependent both on the purpose of the room and on its size. Figure 2 shows how the optimal reverberation time changes for different types of music and for speech. These are typical values and individual preferences may vary from these values by 20% or more.

Figure 2. Dependence of Optimal Reverberation Time on Room Size and Use

1.7 Dependence of Reverberation Time on Frequency

The reverberation time of a room is strongly dependent on frequency. This is because the sound absorption of most materials also strongly depends on frequency. Most people prefer a constant Tr for frequencies above 500 Hz, with substantially increasing reverberation times for lower frequencies. If the reverberation time at low frequencies is too short, the room is usually judged to lack "warmth." If the reverberation time at high frequencies is too short, the room is usually judged to lack "brilliance." Figure 3 shows the most desirable dependence of Tr on frequency (a), and other less desirable behaviors (b and c).

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Figure 3. Dependence of Reverberation Time on Frequency.

Desirable (a) and Undesirable (b and c) Frequency Responses 1.8 Calculation of Reverberation Time

Wallace Sabine developed a simple formula to calculate the reverberation time of a room during his series of studies at Harvard around 1900. The Sabine formula is:

Tr = 0.16 × V

Se Tr is the reverberation time in seconds, V is the volume of the room in m3, and Se is the effective absorption area in m2.

To calculate Se:

(2)

Se = α1S1 + α2S2 + α3S3 + … = ∑ αiSi (3) Se is the total effective absorption area of the room. The individual Si are the areas of each type of material in the room, and the αi are the absorption coefficients for each material.

1.9 Effective Absorption Area

The absorptivity of a material is the proportion of the sound intensity that is not reflected by it. The portion of the sound that is removed may be either absorbed by the material or trans- mitted through it. For the purposes of calculating Tr, it makes no difference which one it is.

A perfect reflector has α = 0, that is, none of the sound intensity which hits the material is absorbed, all of it is reflected. A perfect absorber has α = 1: none of the sound is reflected back into the room.

Real materials have absorption coefficients that range between 0 and 1. This number represents the fraction of the sound that hits the material that is absorbed by it.

The effective absorbing area of any material, then, is the actual area of the material, Si, times its absorption coefficient, αi..

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To calculate the total effective absorbing area of a room, it is necessary to calculate the effective absorbing area of each type of material in the room, and then sum the effective areas. Every object in the room should be included in this calculation.

1.10 Absorption Coefficients

Typical absorption coefficients of some common materials are presented in Table I. Additional absorption coefficients may be found in materials and construction handbooks. It should be noted that αi is strongly dependent on frequency. It is not sufficient to calculate the reverberation time for only one frequency. Tr should be calculated for enough frequencies so that the frequency dependence of Tr is evident, as in Figure 3.

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Table 1. Absorption Coefficients of Some Common Construction Materials

Surface Treatment Absorptivity at Frequency

125 250 500 1000 2000 4000 Acoustic tile, rigidly

mounted 0.2 0.4 0.7 0.8 0.6 0.4

Acoustic tile, suspended in frames

0.5 0.7 0.6 0.7 0.7 0.5

Acoustical Plaster 0.1 0.2 0.5 0.6 0.7 0.7 Ordinary Plaster, on lath 0.2 0.15 0.1 0.05 0.04 0.05 Gypsum wallboard, .5”

on studs 0.3 0.1 0.05 0.01 0.07 0.1

Plywood sheet, .25” on studs

0.6 0.3 0.1 0.1 0.1 0.1

Concrete block, unpainted

0.4 0.4 0.3 0.3 0.4 0.3

Concrete block, painted 0.1 0.05 0.06 0.07 0.1 0.1 Concrete, poured 0.01 0.01 0.02 0.02 0.02 0.03

Brick 0.03 0.03 0.03 0.04 0.05 0.07 Vinyl tile, on concrete 0.02 0.03 0.03 0.03 0.03 0.02

Heavy carpet, on concrete

0.02 0.06 0.015 0.4 0.6 0.6

Heavy carpet, on felt backing

0.1 0.3 0.4 0.5 0.6 0.7

Platform floor, wooden 0.4 0.3 0.2 0.2 0.15 0.1 Ordinary window glass 0.3 0.2 0.2 0.1 0.07 0.04

Heavy glass plate 0.2 0.06 0.04 0.03 0.02 0.02 Draperies, medium

velour 0.07 0.3 0.5 0.7 0.7 0.6

Upholstered seating, unoccupied

0.2 0.4 0.6 0.7 0.6 0.6

Upholstered seating, occupied

0.4 0.6 0.8 0.9 0.9 0.9

Wood/metal seating, unoccupied

0.02 0.03 0.03 0.06 0.06 0.05

Wooden pews, occupied 0.4 0.4 0.7 0.7 0.8 0.7 Sources: Backus (p.172) and L. Doelle, Environmental Acoustics (McGraw-Hill, 1972), p. 227.

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1.11 A Sample Calculation of Tr

Imagine a room that is 3 m high, 10 m long and 15 m wide. The walls are covered with gypsum wallboard, the ceiling is acoustic tile, rigidly mounted, and the floor is covered with heavy carpet on felt backing.

What is the reverberation time for 250 Hz? What is the reverberation time for 2000 Hz?

The volume of the room is: V = 3 m x 10 m x 15 m

V = 450 m2

The areas of the walls is: Front Wall: S1 = 3 m x 15 m = 45 m2

Back Wall: S2 = 3 m x 15 m = 45 m2 Left Side Wall: S3 = 3 m x 10 m = 30m2

Right Side Wall: S4 = 3 m x 10 m = 30 m2

Ceiling: S5 = 10 m x 15 m = 150 m2 Floor: S6 = 10 m x 15 m = 150 m2

For 250 Hz sounds:

Se = α1S1 + α2S2 + α3S3 + α4S4 + α5S5 α6S6

Se = 0.1(45) + 0.1(45) + 0.1(30) + 0.1(30) + 0.4(150) + 0.3(150) (m2)

Se = 4.5 + 4.5 + 3.0 + 3.0 + 60 + 45(m2)

Se = 190.5 m2

Therefore:

Tr = 0.16 sec/m x 450 m3 120.0 m2

Tr = 72 sec/m2

120 m2

Tr = 0.6 sec

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For 2000 Hz sounds:

Se = α1S1 + α2S2 + α3S3 + α4S4 + α5S5 α6S6 And:

Se = 0.07(45) + 0.07(45) + 0.07(30) + 0.07(30) + 0.6(150) + 0.6(150)(m2)

Se = 3.15 + 3.15 + 2.1 + 2.1 + 90 + 90(m2)

Se = 190.5 m2

Tr = 0.16 sec/m x 450 m3 190.5 m2

Tr = 72 sec/m2 190.5 m2

Tr = 0.38 sec

The reverberation times for this room are very short because it was constructed using heavy carpet on the floor and acoustical tile on the ceiling. Judging from the data in Figure 2, it is best suited for speech, and not for any type of music.

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2 Purpose of Laboratory Five In this laboratory, we will measure the reverberation times of several rooms ranging from small (a racquetball court) to large (the Super Pit). We will change the effective absorbing area inside the small room by adding absorbing material such as people and soft materials. We will calculate the expected reverberation time of the racquetball court and compare it to our experimentally determined value. We will also use the experimental data to determine the effective absorbing coefficients of the people and the material.

The purpose of Laboratory 5, Reverberation Time, is to give you personal experience with sensing different reverberation times. This laboratory will also introduce you to how reverberation times can be calculated. Finally, you will see how reverberation times can be changed by careful attention to the construction of the space, including the materials from which it is made.

3 Equipment

The equipment and facilities listed below were used to collect the data. (See note below under “Experimental Procedures.)

• a sound generation device (a waveform generator, for example) • a sound recording system capable of graphic output. (PC running wave software or

equivalent) • access to three rooms with different volumes. We will use:

- racquetball court - classroom space - large arena (the Super Pit)

• software capable of plotting the recorded waveforms as log(SIL) (or dB) versus time • sound absorbing material to place in racquetball court (for example, people and soft

materials).

4 Experimental Procedures

Note: The experiment will not actually be performed. Instead, the results of the experiments will be provided by the Teaching Assistant for student analysis. Students will do calculations only and fill in the worksheet tables using the results.

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Last/First Name (print):

Worksheets: Reverberation Time

Worksheet Table 1

Calculated sabins for a Racquetball Court with a Closed Door at 500 Hz

Surface Area (m2)

α (500 Hz)

Se’ 500 Hz (sabins)

Ceiling 0.02 Floor 0.10 Front 0.02 Back 0.02 Left 0.02

Right 0.02 Totals XXXXX

Worksheet Table 2 Calculated Reverberation Time for a Racquetball Court with a Closed Door at 500 Hz

Court Volume: m3

0.16 x V m3 Total Se (from Table 1) sabins

Tr sec

Worksheet Table 3 Calculated Reverberation Time for a Racquetball Court with an Open Door

Court Volume m3

0.16 x V m3

Previous Se sabins Area of door (sabins)

Total Se sabins Tr sec

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Worksheet Table 4 Data for Modified Reverberation Times

Estimated Area of Door m2

Number of People in the Court

Estimated Area covered by Material m2

Worksheet Table 5 Calculation of the Reverberation Times

Test # Conditions Δt (s) ΔdB Δt / ΔdB Tr (s) 1 Court, noise 2 Court, slapstick 3 Door open, noise 4 Door open, slapstick 5 People in, noise 6 People in, slapstick 7 Material, noise 8 Material, slapstick

*Note: When door is not mentioned in the “Conditions” column, assume door is closed

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Last/First Name (print):

Comparison of Tr Values for Closed vs Open Door

Tr Values Calculation White Noise Slapstick Door closed Door open Difference

Question: Are the calculated and experimental changes in Tr consistent and what you expected? Please explain.

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Worksheet Table 6 Calculation of the Effective Absorbing Area of People at 500 Hz

Court Volume: m3

0.16 x V m3

Calculate Se with no people in the court using the equation:

Se =

0.16V Tr

White Noise Slapstick

Experimental Tr 2 people only (sec)

Calculated Se 2 people only (sabins)

Experimental Tr Many people (sec)

Calculated Se Many people (sabins)

Difference in Se (sabins)

Number of additional People (N – 2)

Se per person (sabins)

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Last/First Name (print):

Worksheet Table 7 Calculation of the Effective Absorbing Area of Soft Material

Added to the Racquetball Court at 500 Hz

Court Volume:

m3

0.16 x V

m3

Without Material Experimental Tr

sec

Without Material Experimental Se

sabins

Repeat the procedure for the data obtained with the material in the court:

With Material Experimental Tr

sec

With Material Experimental Se

sabins

Now calculate the effective absorbing area of the material:

Difference in Se

sabins

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1270 Questionnaire: Experiment 5: Reverberation Time

1. TA name(s):

4. What one thing would you change in this laboratory?

5. What one thing would you leave the same?