sound – propagation
DESCRIPTION
Sound – Propagation. Sound Levels Sound / acoustic waves are pressure waves measured in Pa The amplitude of the wave is usually called the Sound Pressure Level (SPL) The human ear can detect SPL as low as 20 Pa (hearing threshold) The human ear can withstand SPL as high as 60Pa - PowerPoint PPT PresentationTRANSCRIPT
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound – Propagation
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound Levels• Sound / acoustic waves are pressure waves measured in Pa• The amplitude of the wave is usually called the Sound Pressure Level (SPL)• The human ear can detect SPL as low as 20Pa (hearing threshold)• The human ear can withstand SPL as high as 60Pa• The human ear has a dynamic range of 60 / 20x10-6 = 3,000,000• The human ear perceives SPL (nearly) logarithmically:
a 10-fold increase in sound power (or intensity) is needed for a human to perceive a doubling on loudness.
• The dB is based on the hearing threshold (20Pa)• Because acoustic power (P) is proportional to acoustic pressure (p):
2
2 610log 10log 20log 20log20 10ref ref ref
P p p pdBP p p x
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound Levels – decibels
0 10000000 20000000 30000000 40000000 50000000 60000000 700000000
20
40
60
80
100
120
140
Sound pressure [Pa]
dB
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound Levels – decibels
0 1,000,000 2,000,000 3,000,000 4,000,0000
20
40
60
80
100
120
140
Sound pressure ratio [reference: 20 Pa]
dB
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound Levels – decibels
10 100 1000 10000 100000 1000000 10000000 1000000000
20
40
60
80
100
120
140
Sound pressure [Pa]
dB
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound Levels – Examples:• The measured SPL in a room is 40Pa. What is the Sound level in dB?
6
6 6
40 1020log 20log 20log 2 620 10 20 10p xdB dBx x
20log 10 20dB dB
20log 100 40dB dB
6
1806 6 6 9 320 20
20log20 10
20 10 10 20 10 10 20 10 10 20 10dB
pdBx
p x x x x x Pa
• At the launch of India’s Polar Satellite Launch Vehicle (PSLV) rocket, you measure the sound level at 170 dB. How much acoustic pressure is measured by your microphone?
• The volume of a music player is increased by 10, what is the change in dB?
• The volume of a music player is increased by 100, what is the change in dB?
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• A rich sound is produced in a room and suddenly stopped. Calculate the
reverberation time from the recorded acoustic pressure shown below:
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 9-50
0
50
100
Elapsed time [s]
Mag
nitu
de [d
B]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Remember: Reverberation time = time taken for sound to decrease by 60 dB
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 9-50
0
50
100
Elapsed time [s]
Mag
nitu
de [d
B]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Step 1: Compute moving RMS (Root-Mean-Square)• Note: Must select window width (in seconds)
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 9-50
0
50
100
Elapsed time [s]
Mag
nitu
de [d
B]
Moving RMS [Pa]
Recorded sound [Pa]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Step 2: Transform moving RMS into dB and plot
Moving RMS [Pa]
Recorded sound [Pa]
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 9-50
0
50
100
Elapsed time [s]
Mag
nitu
de [d
B]
Moving RMS [dB]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Step 3: Zoom in dB vs time curve if necessary
Moving RMS [Pa]
Recorded sound [Pa]
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
4 4.5 5 5.5 6 6.520
40
60
80
100
Elapsed time [s]
Mag
nitu
de [d
B]
Reverberation Time:0.82327 [s]
Moving RMS [dB]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Step 4: Select range (domain) for analysis
Moving RMS [Pa]
Recorded sound [Pa]
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8
30
40
50
60
70
80
90
Elapsed time [s]
Mag
nitu
de [d
B]
Reverberation Time:0.82327 [s]
SelectedRange foranalysis
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation time – Example:• Step 5: Compute slope of dB vs time curve (straight line of best fit)
• Step 5: Compute Reverberation Tine (RT):RT=60/slope [s]
Moving RMS [Pa]
Recorded sound [Pa]
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6
30
40
50
60
70
80
90
Elapsed time [s]
Mag
nitu
de [d
B]
Reverberation Time:0.82327 [s]
Straight line of best fit: Slope [dB/s]
ENF1104 Problem Solving for Engineers – Acoustic Project
Reverberation Time – Example output from analysis software:
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 920
40
60
80
100
Elapsed time [s]
Mag
nitu
de [d
B]
Reverberation Time:0.82327 [s]
0 1 2 3 4 5 6 7 8 9
-0.5
0
0.5
Elapsed time [s]
Sou
nd P
ress
ure
[-]
0 1 2 3 4 5 6 7 8 920
40
60
80
100
Elapsed time [s]
Mag
nitu
de [d
B]
Reverberation Time:0.82327 [s]
Moving RMS [Pa]
Recorded sound [Pa]
Moving RMS [dB]Decay slope [dB/s]
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound – Hearing threshold
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound – Hearing range
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound - Octaves• Partitioning the frequency scale is a long-standing practice based on music• The octave is base of doubling or halving the frequency• Smaller increments are used for musical instruments (eg: piano) such as 1/3 or
1/12 octave• The reverberation time of a room may vary depending on the frequency of the
sound (dependent of the type of material that absorbs sound0• Too much time / effort required to evaluate RT for small frequency bands
(increments) over very large hearing range (20 – 20,000 Hz)• For practical purposes Octave Bands are used
ENF1104 Problem Solving for Engineers – Acoustic Project
Sound – Octaves bands
Lower limit (Hz)
(÷2)
Centre Frequency [Hz]
Upper limit (Hz)
(x2)
44 63 88
88 125 177
177 250 354
354 500 707
707 1000 1414
1414 2000 2828
2828 4000 5657
5657 8000 11314