The decibel scale

Projectile motion - 1
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The decibel scale
• Sound intensity
• Sound level: The decibel scale
• Sound level calculations
• Some decibel measurements
• Change in intensity
• Human hearing
• The Phon scale
The decibel scale - 2
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Sound intensity
• The intensity of sound decreases with the square of the distance from
the source.
power
Sound intensity =
area
P
2
I = (unit =W /m )
A
2
P
I=
2
4πr
The decibel scale - 3
I2  r1 
= 
I1  r2 
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Sound intensity
• eg a sound source emitting a power of 1 mW, when heard at a distance
of 1 vs 2 m
−3
P 1×10 W
−5
2
I= =
= 8×10 W /m
2
A 4 π (1m )
−3
P 1×10 W
−5
2
I= =
=2×10 W /m
2
A 4 π (2m )
The decibel scale - 4
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Sound level: The decibel scale
• The decibel scale is a relative scale, based upon the threshold of
hearing I0 = 10-12 W/m2.
• It is a logarithmic scale, an increase of 10 corresponds to 10 times
the intensity.
• 20dB = 102 times, 30dB = 103 times the intensity.
L =10log
I
I0
I =10
 L

−12


 10

W /m
2
I
L =10log −12
10
The decibel scale - 5
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Sound level calculations
• eg A sound has the intensity of 10-4 W/m2. This is a sound level of
−4
I
10
8
L =10log =10log −12 =10log10 = 80dB
I0
10
eg The intensity of a 45 dB sound is
I =10
 L

 −12
 10

=10
 45

 −12
 10

=10
−7.5
−8
= 3.2×10 W /m
2
What is the intensity of 120 dB?
I =10
The decibel scale - 6
 L

 −12
 10

=10
 120

−12

 10

0
=10 =1W /m
2
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Some decibel measurements
Source
Threshold of hearing
Soft whisper
Quiet conversation
Loud conversation
Highway traffic
Tractor engine
Threshold of pain (Rock concert)
Jet engine (less than 50 m away)
Rocket launch (less than 500 m away)
Intensity (W/m2)
10-12
10-10
10-8
10-6
10-4
10-2
10-0 (1)
102 (100)
104 (10,000)
Sound level (dB)
0 dB
20 dB
40 dB
60 dB
80 dB
100 dB
120 dB
140 dB
160 dB +
• Damage to hearing is due to both the sound level & exposure time.
• The biggest risk to hearing loss for most young people today is loud
headphones!
The decibel scale - 7
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Change in intensity
I2
I1
ΔL =L2 −L1 =10log −10log
I0
I0
I2
ΔL =10log
I1
Double intensity:
ΔL =10log2 ≈ +3dB
1
Half intensity: ΔL =10log = −10log2 ≈ −3dB
2
Doubling the distance from a source gives one quarter of the intensity:
1
ΔL =10log = −10log4 ≈ −6dB
4
The decibel scale - 8
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Human Hearing
• The human ear can hear sounds from ~20 Hz → 20 kHz
• Our ears are most responsive to frequencies ~2-3 kHz
• As we age, we lose sensitivity to the higher frequencies.
• The dBA & Phon scales is weighted so that a reading is of equal
perceived loudness regardless of frequency.
The decibel scale - 9
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The phon scale
• The phon scale shows how human ears respond to sounds at different
frequencies.
• Different frequencies at the same Phon level are perceived to be equally
loud.
• Based on the perception of 1kHz at different intensities.
• Sounds at 2 - 3 kHz are generally the loudest to our ears.
• At higher intensities, the dB differences between perceived equally
loud sounds are less.
The decibel scale - 10
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The phon scale
120 Phon
110 Phon
120
Sound pressure level (dB)
110
100 Phon
100
90 Phon
80 Phon
90
80
70 Phon
60 Phon
50 Phon
70
60
50 Hz: 50dB
50
40 Phon
30 Phon
20 Phon
10 Phon
40
30
20
10
1 kHz: 10dB
0
50
The decibel scale - 11
100 200
500
1k 2k
Frequency (Hz)
5k
10k 20k
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Projectile motion - 12
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