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β dB = 10 log 10 I I 0 , size 12{β left ("dB" right )="10""log" rSub { size 8{"10"} } left ( { {I} over {I rSub { size 8{0} } } } right )} {}

where I 0 = 10 –12 W/m 2 size 12{I rSub { size 8{0} } ="10" rSup { size 8{ - "12"} } "W/m" rSup { size 8{2} } } {} is a reference intensity. In particular, I 0 size 12{I rSub { size 8{0} } } {} is the lowest or threshold intensity of sound a person with normal hearing can perceive at a frequency of 1000 Hz. Sound intensity level is not the same as intensity. Because β size 12{β} {} is defined in terms of a ratio, it is a unitless quantity telling you the level of the sound relative to a fixed standard ( 10 –12 W/m 2 size 12{"10" rSup { size 8{ - "12"} } "W/m" rSup { size 8{2} } } {} , in this case). The units of decibels (dB) are used to indicate this ratio is multiplied by 10 in its definition. The bel, upon which the decibel is based, is named for Alexander Graham Bell, the inventor of the telephone.

Sound intensity levels and intensities
Sound intensity level β (dB) Intensity I (W/m 2 ) Example/effect
0 1 × 10 –12 Threshold of hearing at 1000 Hz
10 1 × 10 –11 Rustle of leaves
20 1 × 10 –10 Whisper at 1 m distance
30 1 × 10 –9 Quiet home
40 1 × 10 –8 Average home
50 1 × 10 –7 Average office, soft music
60 1 × 10 –6 Normal conversation
70 1 × 10 –5 Noisy office, busy traffic
80 1 × 10 –4 Loud radio, classroom lecture
90 1 × 10 –3 Inside a heavy truck; damage from prolonged exposure Several government agencies and health-related professional associations recommend that 85 dB not be exceeded for 8-hour daily exposures in the absence of hearing protection.
100 1 × 10 –2 Noisy factory, siren at 30 m; damage from 8 h per day exposure
110 1 × 10 –1 Damage from 30 min per day exposure
120 1 Loud rock concert, pneumatic chipper at 2 m; threshold of pain
140 1 × 10 2 Jet airplane at 30 m; severe pain, damage in seconds
160 1 × 10 4 Bursting of eardrums

The decibel level of a sound having the threshold intensity of 10 12 W/m 2 size 12{"10" rSup { size 8{ - "12"} } "W/m" rSup { size 8{2} } } {} is β = 0 dB size 12{β=0"dB"} {} , because log 10 1 = 0 size 12{"log" rSub { size 8{"10"} } 1=0} {} . That is, the threshold of hearing is 0 decibels. [link] gives levels in decibels and intensities in watts per meter squared for some familiar sounds.

One of the more striking things about the intensities in [link] is that the intensity in watts per meter squared is quite small for most sounds. The ear is sensitive to as little as a trillionth of a watt per meter squared—even more impressive when you realize that the area of the eardrum is only about 1 cm 2 , so that only 10 16 size 12{"10" rSup { size 8{ - "16"} } } {} W falls on it at the threshold of hearing! Air molecules in a sound wave of this intensity vibrate over a distance of less than one molecular diameter, and the gauge pressures involved are less than 10 9 size 12{"10" rSup { size 8{ - 9} } } {} atm.

Another impressive feature of the sounds in [link] is their numerical range. Sound intensity varies by a factor of 10 12 size 12{"10" rSup { size 8{"12"} } } {} from threshold to a sound that causes damage in seconds. You are unaware of this tremendous range in sound intensity because how your ears respond can be described approximately as the logarithm of intensity. Thus, sound intensity levels in decibels fit your experience better than intensities in watts per meter squared. The decibel scale is also easier to relate to because most people are more accustomed to dealing with numbers such as 0, 53, or 120 than numbers such as 1 . 00 × 10 11 size 12{1 "." "00" times "10" rSup { size 8{ - "11"} } } {} .

One more observation readily verified by examining [link] or using I = ( Δ p ) 2 ρv w 2 is that each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB sound is 30 dB greater, or three factors of 10 (that is, 10 3 times) as intense. Another example is that if one sound is 10 7 as intense as another, it is 70 dB higher. See [link] .

Questions & Answers

what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
what is radioactive element
Half of the total time required by a radioactive nuclear atom to totally disintegrate
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
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state the laws of refraction
state laws of reflection
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when was the name taken from
Biola Reply
retardation of a car
when was the name retardation taken
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Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
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Amey Reply
Black body is the ideal body can absorb and emit all radiation
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that is photoelectric effect ?
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It is the emission of electrons when light hits a material
is not just a material
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agangan Reply
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Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
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light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
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same units of energy
what is same units of energy?
M L2 T -2
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M L2 T-2
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an object of mass 200g moves along a circular path of radius 0.5cm with a speed of 2m/s. calculate the angular velocity ii period iii frequency of the object
Faith Reply
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-- Reply
Practice Key Terms 3

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