<< Chapter < Page Chapter >> Page >
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 ohm's law
Pamilerin Reply
states that electric current in a given metallic conductor is directly proportional to the potential difference applied between its end, provided that the temperature of the conductor and other physical factors such as length and cross-sectional area remains constant. mathematically V=IR
ANIEFIOK
A body travelling at a velocity of 30ms^-1 in a straight line is brought to rest by application of brakes. if it covers a distance of 100m during this period, find the retardation.
Pamilerin Reply
what is distribution of trade
Grace Reply
what's acceleration
Joshua Reply
The change in position of an object with respect to time
Mfizi
Acceleration is velocity all over time
Pamilerin
hi
Stephen
It's not It's the change of velocity relative to time
Laura
Velocity is the change of position relative to time
Laura
acceleration it is the rate of change in velocity with time
Stephen
acceleration is change in velocity per rate of time
Noara
what is ohm's law
Stephen
Ohm's law is related to resistance by which volatge is the multiplication of current and resistance ( U=RI)
Laura
how i don understand
Willam Reply
how do I access the Multiple Choice Questions? the button never works and the essay one doesn't either
Savannah Reply
How do you determine the magnitude of force
Peace Reply
mass × acceleration OR Work done ÷ distance
Seema
Which eye defect is corrected by a lens having different curvatures in two perpendicular directions?
Valentina Reply
acute astigmatism?
the difference between virtual work and virtual displacement
Noman Reply
How do you calculate uncertainties
Ancilla Reply
What is Elasticity
Salim Reply
using a micro-screw gauge,the thickness of a piece of a A4 white paper is measured to be 0.5+or-0.05 mm. If the length of the A4 paper is 26+or-0.2 cm, determine the volume of the A4 paper in: a). Cubic centimeters b). Cubic meters
Ancilla Reply
what is module
Alex Reply
why it is possible for an object(man) to stay on air without falling down?
akande Reply
its impossible, what do you mean exactly?
Ryan
Exactly
Emmanuella
it's impossible
Your
Why is it not possible to stand in air?
bikko
the air molecules are very light enough to oppose the gravitational pull of the earth on the man..... hence, freefall occurs
Arzail
because of gravitational forces
Pamilerin
this mostly occur in space
Stephen
what is physics
Joshua Reply
no life without physics ....that should tell you something
Exactly
Emmanuella
😎👍
E=MC^2
study of matter and energy and an inter-relation between them.
Minahil
that's how the mass and energy are related in stationery frame
Arzail
Ketucky tepung 10m
firdaus
Treeskin, 6m Cloud gam water 2m Cloud gam white 2m And buur
firdaus
Like dont have but have
firdaus
Two in one
firdaus
Okay
firdaus
DNA card
firdaus
hey am new over hear
Shiwani
War right? My impesilyty again. Don't have INSURAN for me
firdaus
PUSH
firdaus
I give
firdaus
0kay
firdaus
Hear from long
firdaus
Hehehe
firdaus
All physics... Hahahaha
firdaus
Tree skin and two cloud have tokside maybe
firdaus
Sold thing
firdaus
PUSH FIRST. HAHAHAAHA
firdaus
thanks
firdaus
Kinetic energy is the energy due to montion of waves,electrons,atoms, molecule,substances an object s.
Emmanuella
Opjective 0
firdaus
Atom nber 0
firdaus
SOME N
firdaus
10.000m permonth. U use momentom with me
firdaus
hi
Hilal
plz anyone can tell what is meteor and why meteor fall in night? can meteor fall in the day
Hilal
meteor are the glowy (i.e. heated when the enter into our atmosphere) parts of meteoroids. now, meteoroids are the debris resulting from the collision of asteroids or comets. yes, it occurs in daytime too, but due to the daylight, we cant observe it as clearly as in night
Arzail
thank's
Hilal
hello guys
Waka
wich method we use to find the potential on a grounded sphere
Noman
hello
Pamilerin
Physics is the science that studies everything around us from the smallest things like quarks to the biggest things like galaxies. It's simply everything.
Laura
Good day everyone
Divine
It talks mainly about matter with related topics such as forces energy gravity and time. It's amazing
Laura
Hi
Alpha
Physics generally is the study of everything around us.
Steven
physics is the branch of sceince
shafiu
physics is the branch of sceince that deal with motion
shafiu
physics is the branch of sceince that deal with motion &energy
shafiu
Practice Key Terms 3

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask