Ottorino Respighi
(1879 - 1936)

Energy in Waves

Energy in Waves

Power
E = Energy
t = Time
P = Power
  P = E/t
=Joule/s = Watt = W

Examples
Gasoline
Solar Energy

Intensity
P = Power
S = Surface Area
I = Intensity
I = P/S  (W/m2)

Intensity
Example: over a 5 minute period 3 x 105 Joules of energy from the sun hit a surface.  What is the power?

Intensity and Distance
I2/I1 = (r1/r2)2
or
I ~ 1/r2

Examples
Audio demo Track 11
If the Intensity at 25 cm was 8 x 10-6 W/m2, what are the intensities at 50 cm, 1 m, and 2 m?

Sound Intensity
Sound Source         Intensity (W/m2)
Saturn rocket at 50 m                                     108
Jet engine at 10 m                                            103
Jet engine at 50 m                                            10
SST takeoff at 500 m; Pneumatic drill          100 = 1
Amplified Rock Music                                   10-1
Machine shop                                                  10-2
Jackhammer at 1 m; Subway train                10-3
Factory                                                              10-4

Sound Intensity
Sound Source         Intensity (W/m2)
City traffic                                                        10-5
Normal conversation at 1 m                          10-6
Office; Classroom; Quiet auto interior        10-7
Library                                                              10-8
Empty auditorium; City street, no traffic    10-9
Whisper at 1 m                                                10-10
Rustle of leaves; Falling pin                          10-11
Limit of audibility                                           10-12

Sound Intensity Level (SIL)
If I2/I1 = 10, then,
by definition
SIL2 - SIL1 = 10 dB

SIL Difference
SIL2 - SIL1 = 10 log(I2/I1)
thus if
SIL2 - SIL1 = 20 then I2/I1=100
SIL2 - SIL1 = 30 then I2/I1=1000
SIL2 - SIL1 = 40 then I2/I1=10,000

Sound Intensity/SIL
Sound Source               Intensity/SIL
Saturn rocket at 50 m                                   108   = 200 dB
Jet engine at 10 m                                         103    = 150 dB
Jet engine at 50 m                                         10     = 130 dB
SST takeoff at 500 m; Pneumatic drill       100    = 120 dB
Amplified Rock Music                                 10-1  = 110 dB
Machine shop                                                10-2  = 100 dB
Jackhammer at 1 m; Subway train             10-3  =   90 dB
Factory                                                            10-4  =    80 dB

Sound Intensity/SIL
Sound Source                         Intensity/SIL
City traffic                                                       10-5   = 70 dB
Normal conversation at 1 m                         10-6   = 60 dB
Office; Classroom; Quiet auto interior        10-7   = 50 dB
Library                                                             10-8   = 40 dB
Empty auditorium; City street, no traffic   10-9   = 30 dB
Whisper at 1 m                                                10-10 = 20 dB
Rustle of leaves; Falling pin                          10-11 = 10 dB
Limit of audibility                                          10-12  =   0 dB

Examples
Two sounds have a ratio of intensities of 4,700.  Find the difference in SIL for the two sounds.
If the difference in SIL for two sounds is 8 dB, what is the ratio of the intensities?

Examples
Audio demo Tracks 8-10

SIL and the Ear
SIL (dB)    Occupational                Occasional
     80            No limit                         4 hours
     85            No limit                         2 hours
     90            8 hours                           1 hour
     95            4 hours                           30 minutes
   100            2 hours                           15 minutes
   105            1 hour                               8 minutes
   110            30 minutes                       4 minutes
   115            15 minutes                       2 minutes

SILs in Music
In traditional music, the sound intensity level is usually in the range of 45 to 95 dB.
dB meter

Combined Sounds
What happens if we add a 60 dB sound to a 70 dB sound?
60 dB + 70 dB \ 120 dB!!!
Instead, Intensities Add.
Ic = I1 + I2

Combined Sounds
What happens if we add a total of n sources of sound having the same SIL?