Loudness

1
Loudness

• Power, intensity, intensity level,

2
Power and intensity
Sound detector
1J1Nm
Energy will accumulate in time
1W1J/s
Power rate of energy transfer, stays the same
Dependent on detector area
1 W/m21J/sm2
Intensity rate of energy transfer per area
3
Inverse Square Law
B
radius B 2 radius A
A
area B 4 area A
intensity B 1/4 intensity A
4
Sound intensity level

• Physiological response to loudness does not
  simply scale with intensity
• Loudest possible sound waves
• 1 Watt / square meter
• Softest perceptible sound
• 10-12 Watt / square meter
• Chosen as reference intensity

5
Sound intensity level

• 1 Decibel1/10 bel (Alexander Graham Bell)
• 1 bel for a sound means
• the ratio of its intensity to a reference is 101

Decibel measure the relation between two sounds,
not an amount of sound.
6
Chart of sound levels
source L (dB) I (W/m2) reaction
0 10-12 inaudible
Empty auditorium 30 10-9
Library 40 10-8
conversation 60 10-6
Factory 80 10-4
Amplified Rock 110 10-1 Painful
7
Sound level and music

• More than 50 dB (eliminates background)
• Above 100 dB damage to ears
• ffff (95 dB) to ppp (50 dB)
• More likely 6085 dB for symphony concert
• Determined by range of instruments (typically lt
  40dB)
• Wood-wind only 10 dB dynamic range

8
Sound levels and multiple sources
What is the resulting sound level L?
Violinist A IA60 dB
Violinist B IB60 dB
10-6 W/m2
10-6 W/m2
(60Log2) dB 63 dB
210-6 W/m2
9
Sound levels and multiple sources
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
10-6 W/m2
What is the resulting sound level L?
1010-6 W/m2
70 dB
10-5 W/m2