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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

find the density of a fluid in which a hydrometer having a density of 0.750g/mL floats with 92.0% of its volume submerged.
Neshrin Reply
Uniform speed
Sunday
(a)calculate the buoyant force on a 2.00-L Helium balloon.(b) given the mass of the rubber in the balloon is 1.50g. what is the vertical force on the balloon if it is let go? you can neglect the volume of the rubber.
Neshrin Reply
To Long
Usman
pleaseee. can you get the answer? I can wait till 12
Neshrin
a thick glass cup cracks when hot liquid is poured into it suddenly
Aiyelabegan Reply
because of the sudden contraction that takes place.
Eklu
railway crack has gap between the end of each length because?
Aiyelabegan Reply
For expansion
Eklu
yes
Aiyelabegan
Please i really find it dificult solving equations on physic, can anyone help me out?
Big Reply
sure
Carlee
what is the equation?
Carlee
Sure
Precious
fersnels biprism spectrometer how to determined
Bala Reply
how to study the hall effect to calculate the hall effect coefficient of the given semiconductor have to calculate the carrier density by carrier mobility.
Bala
what is the difference between atomic physics and momentum
Nana Reply
find the dimensional equation of work,power,and moment of a force show work?
Emmanuel Reply
What's sup guys
Peter
cul and you all
Okeh
cool you bro
Nana
so what is going on here
Nana
hello peeps
Joseph
Michelson Morley experiment
Riya Reply
how are you
Naveed
am good
Celine
you
Celine
hi
Bala
Hi
Ahmed
Calculate the final velocity attained, when a ball is given a velocity of 2.5m/s, acceleration of 0.67m/s² and reaches its point in 10s. Good luck!!!
Eklu Reply
2.68m/s
Doc
vf=vi+at vf=2.5+ 0.67*10 vf= 2.5 + 6.7 vf = 9.2
babar
s = vi t +1/2at sq s=58.5 s=v av X t vf= 9.2
babar
how 2.68
babar
v=u+at where v=final velocity u=initial velocity a=acceleration t=time
Eklu
the answer is 9.2m/s
OBERT
express your height in Cm
Emmanuel Reply
my project is Sol gel process how to prepare this process pls tell me
Bala
the dimension of work and energy is ML2T2 find the unit of work and energy hence drive for work?
Emmanuel Reply
KgM2S2
Acquah
Two bodies P and Quarter each of mass 1000g. Moved in the same direction with speed of 10m/s and 20m/s respectively. Calculate the impulse of P and Q obeying newton's 3rd law of motion
Shimolla Reply
kk
Doc
the answer is 0.03n according to the 3rd law of motion if the are in same direction meaning they interact each other.
OBERT
definition for wave?
Doc Reply
A disturbance that travel from one medium to another and without causing permanent change to its displacement
Fagbenro
In physics, a wave is a disturbance that transfers energy through matter or space, with little or no associated mass transport (Mass transfer). ... There are two main types ofwaves: mechanical and electromagnetic. Mechanicalwaves propagate through a physical matter, whose substance is being deformed
Devansh
K
Manyo
thanks jare
Doc
Thanks
AMADI
Note: LINEAR MOMENTUM Linear momentum is defined as the product of a system’s mass multiplied by its velocity: size 12{p=mv} {}
AMADI
what is physic
zalmia Reply
please gave me answar
zalmia
Study of matter and energy
Fagbenro
physics is the science of matter and energy and their interactions
Acquah
physics is the technology behind air and matter
Doc
Okay
William
hi sir
Bala
how easy to understanding physics sir
Bala
Easy to learn
William
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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