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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
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
Atomic transmutation
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
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
Ahmed
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Busayo
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
Anita
Yeah
yusuf
is not just a material
Neemat
it is the surface of a metal
Neemat
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
Awene
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
babels
pls what is mirage
babels
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
Deepika
what is the dimensional formula for torque
Otto Reply
L2MT-2
Jolly
same units of energy
Baber
what is same units of energy?
Baber
Nm
Sphere
Ws
Sphere
CV
Sphere
M L2 T -2
Dokku
it is like checking the dimension of force. which is ML2T-2
Busayo
ML2T-2
Joshua
M L2 T-2
Samuel
what is the significance of moment of inertia?
study
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
w = 2/(0.005) period = PIE(0.005) f = 1/(PIE(0.005)) assuming uniform motion idk..
Georgie
w=2/(0.005)×100
isaac
supposed the speed on the path is constant angular velocity w (rad/s) = v (m/s) : R (m) period T (s) = 2*Pi * R : v frequency f ( Hz) = 1: T
Sphere
a=w.w.r=mv.v/r,w=mv/r=0.2×2/0.005=80rads-s
Mac
in the pole vaulter problem, how do they established that the mass is 5.00kg? where did that number come from?
-- Reply
Practice Key Terms 3

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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