The Single Event Level The Single Event Level SELSEL

The Single Event Level The Single Event Level

SEL SEL

Angelo Farina

Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, 43100 Parma – Italy

angelo.farina@unipr.it

The Equivalent Continuous Level (L

The Equivalent Continuous Level (L

): ):

 





 



  

rif T

eq

dt

p t p L T

0

2 2 ,

) ( log 1

10

The continuous equivalent level Leq (dB) is defined as:

where T is the total measurement time, p(t) is the instantaneous pressure value and p_rif is the reference pressure

• L_eq,T  dB (linear frequency weighting)

• L_Aeq,T  dB(A) (“A” weighting)

Definition of SEL (Single Event Level) Definition of SEL (Single Event Level)

s T T

Leq T

SEL 10 log ₀ 1

0

10  



 



 





the SEL is the equivalent level packed in one second

Definition of SEL (Single Event Level) Definition of SEL (Single Event Level)

the SEL is the equivalent level packed in one second SEL

1s

Example of SEL (Single Event Level) Example of SEL (Single Event Level)

Time history of the passage of an aircraft

45 55 65 75 85 95

Livello Sonoro in dB(A)

0 10 20 30 40 50

Tempo (s)

Fokker 50 - Esponenziale - FAST

Noise from roads and railways Noise from roads and railways

Angelo Farina

Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, 43100 Parma – Italy

angelo.farina@unipr.it

Contnuous Line Sources Contnuous Line Sources

Many noise sources found outdoors can be considered line sources: roads, railways, airtracks, etc.

Geometry for propagation from a line source to a receiver - in this case the total power is dispersed over a cylindrical surface:

d

R

r

dx X

O

) (

8 log

10

) (

6 log

10

emission coherent

d L

L

emission incoherent

d L

L

W p

W p

















In which Lw’ is the sound power level per meter of line source









 

 dx

r

I W

4

'



Coherent cylindrical field Coherent cylindrical field

• The power is dispersed over an infinitely long, pulsating cylinder:

   

 

r lg 10 2

lg W 10

L lg W W 10

W I r L 2

W lg

I r L 10 2

W lg

I 10 lg I 10 L

L r 2

W S

I W

W I

o o

o o

o o

I























 





 



















 





 

























 

 



 



 









 



r

L

In which Lw’ is the sound power level per meter of line source

“ “ discrete discrete ” ” (and incoherent) linear sources (and incoherent) linear sources

Another common case is when a number of point sources are located along a line, each emitting sound mutually incoherent with the others:

Geometry of propagation for a discrete line source and a receiver

- We could compute the SPL at the receiver as the energetic (incoherent) summation of many spherical wavefronts. But at the end the result shows that SPL decays with the same cylindrical law as with a coherent source:

Lw’

Note that the incoherent SPL is 2 dB louder than the coherent one!

d

R

 1

r 1 r i

S

r i-1

 i

a

  ^{a 10 log}   ^{d 6 [ dB ]}

log 10

L

L _p  _Wp   

A road is a sequence of point sources A road is a sequence of point sources

d

V (km/h)

EXAMPLE:

• V = 50 km/h

• Q = 500 vehicles/h

• L

= 90 dB(A) Hence:

• d = V/Q = 50000/500 = 100 m

• L

’ = L

– 10·log

(d) = 90 – 10·log

(100) = 70 dB(A) Consequently, at a distance r = 50 m, we get:

• L

= L

’ – 10·log

(r) – 6 = 70 – 10·log

(50) – 6 = 47 dB(A)

Definition of SEL (Single Event Level) Definition of SEL (Single Event Level)

s T T

Leq T

SEL 10 log

1

0

10

 



 



 





The SEL is the equivalent level packed in one second

45 55 65 75 85 95

Livello Sonoro in dB(A)

0 10 20 30 40 50

Tempo (s)

Fokker 50 - Esponenziale - FAST

Leq SEL

Relationship between SEL and Lw’

Relationship between SEL and Lw’

  ⁶

log 1000 10

log

10

1

.

   



 





 





V L Q

Leq _{W vehicle}

  ^{7 . 5 6 10 log}  ³⁶⁰⁰ 

log 1000 10

log 1

10

  

  



 





 



 Lw V

SEL

We did find that:

SEL is measured at the standard distance r = 7.5 m, and referes to just one of the Q vehicles passing each hour, packed in one second:

  ^{9 . 19}

log

10 





 Lw V

SEL

When V=50 km/h, we get:

SEL = Lw – 26.19 dB(A)

For a constant value of Lw, SEL decreases with the speed of vehicles V

Computing the time profile Computing the time profile

r

R

r’(x) O x

Lw

v (m/s) v·t

   

    ¹¹

log 10

) (

11 '

log 10

) (

2 2 10

2 10





















t v r

Lw t

Lp

t r Lw

t Lp

Effect of vehicle’s speed Effect of vehicle’s speed

Sound Power Level Lw increases with speed above 30 km/h

Effect of vehicle’s speed Effect of vehicle’s speed

6 dB/radd.

Engine

Rolling

Aerodynamics

Time profile vs vehicle’s speed Time profile vs vehicle’s speed

Increasing the speed the profile becomes shorter and higher

SEL vs vehicle’ speed SEL vs vehicle’ speed

3 dB/radd.

-3 dB

/radd.

SEL vs vehicle’ speed SEL vs vehicle’ speed

SEL has a minimum around 70 km/h

Definition of personal exposure level (L

Definition of personal exposure level (L

): ):

 

 



  

0 2 rif 2

ep

dt

p ) t ( p h 8 log 1 10 L

The personal exposure level Lep (dB) is defined as:

where 8h is the standardised duration of a work day. Hence:

8h

Lep

 

 





 h

L T L _{ep eq}

log 8

10

Example of L

Example of L

computation: computation:

1h 1h 2h 3h 1h 2h

75 80

75

84

75 78

h dB L

h dB L

ep eq

4 . 8 81

10 2 10

1 10

3 10

2 10

1 10

log 1 10

4 . 10 80

10 2 10

1 10

3 10

2 10

1 10

log 1 10

8 . 7 5

. 7 4

. 8 5

. 7 0

. 8 5

. 7

8 . 7 5

. 7 4

. 8 5

. 7 0

. 8 5

. 7

 



 



           





 



 



           



