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The sound intensity level     β of a sound, measured in decibels , having an intensity I in watts per meter squared, is defined as

β ( dB ) = 10 log 10 ( I I 0 ) ,

where I 0 = 10 −12 W/m 2 is a reference intensity, corresponding to the threshold intensity of sound that a person with normal hearing can perceive at a frequency of 1.00 kHz. It is more common to consider sound intensity levels in dB than in W/m 2 . How human ears perceive sound can be more accurately described by the logarithm of the intensity rather than directly by the intensity. Because 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 ). 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.

The decibel level of a sound having the threshold intensity of 10 −12 W/m 2 is β = 0 dB, because log 10 1 = 0 . [link] gives levels in decibels and intensities in watts per meter squared for some familiar 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 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 atm .

[1] 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.
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 [1]
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

An observation readily verified by examining [link] or by using [link] 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 ( [link] ).

Ratios of intensities and corresponding differences in sound intensity levels
I 2 / I 1 β 2 β 1
2.0 3.0 dB
5.0 7.0 dB
10.0 10.0 dB
100.0 20.0 dB
1000.0 30.0 dB

Calculating sound intensity levels

Calculate the sound intensity level in decibels for a sound wave traveling in air at 0 °C and having a pressure amplitude of 0.656 Pa.


We are given Δ p , so we can calculate I using the equation I = ( Δ p ) 2 2 ρ v w . Using I , we can calculate β straight from its definition in β ( d B ) = 10 log 10 ( I I 0 ) .


  1. Identify knowns:
    Sound travels at 331 m/s in air at 0 °C .
    Air has a density of 1.29 kg/m 3 at atmospheric pressure and 0 °C .
  2. Enter these values and the pressure amplitude into I = ( Δ p ) 2 2 ρ v .
    I = ( Δ p ) 2 2 ρ v = ( 0.656 Pa ) 2 2 ( 1.29 kg/m 3 ) ( 331 m/s ) = 5.04 × 10 −4 W/m 2 .
  3. Enter the value for I and the known value for I 0 into β ( dB ) = 10 log 10 ( I / I 0 ) . Calculate to find the sound intensity level in decibels:
    10 log 10 ( 5.04 × 10 8 ) = 10 ( 8.70 ) dB = 87 dB .


This 87-dB sound has an intensity five times as great as an 80-dB sound. So a factor of five in intensity corresponds to a difference of 7 dB in sound intensity level. This value is true for any intensities differing by a factor of five.

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Questions & Answers

In Example, we calculated the final speed of a roller coaster that descended 20 m in height and had an initial speed of 5 m/s downhill. Suppose the roller coaster had had an initial speed of 5 m/s uphill instead, and it coasted uphill, stopped, and then rolled back down to a final point 20 m bel
tan Reply
A steel lift column in a service station is 4 meter long and .2 meter in diameter. Young's modulus for steel is 20 X 1010N/m2.  By how much does the column shrink when a 5000- kg truck is on it?
Andiswa Reply
what exactly is a transverse wave
Dharmee Reply
does newton's first law mean that we don't need gravity to be attracted
Dharmee Reply
no, it just means that a brick isn't gonna move unless something makes it move. if in the air, moves down because of gravity. if on floor, doesn't move unless something has it move, like a hand pushing the brick. first law is that an object will stay at rest or motion unless another force acts upon
yeah but once gravity has already been exerted .. i am saying that it need not be constantly exerted now according to newtons first law
gravity is constantly being exerted. gravity is the force of attractiveness between two objects. you and another person exert a force on each other but the reason you two don't come together is because earth's effect on both of you is much greater
maybe the reason we dont come together is our inertia only and not gravity
this is the definition of inertia: a property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.
the earth has a much higher affect on us force wise that me and you together on each other, that's why we don't attract, relatively speaking of course
quite clear explanation but i just want my mind to be open to any theory at all .. its possible that maybe gravity does not exist at all or even the opposite can be true .. i dont want a fixed state of mind thats all
why wouldn't gravity exist? gravity is just the attractive force between two objects, at least to my understanding.
earth moves in a circular motion so yes it does need a constant force for a circular motion but incase of objects on earth i feel maybe there is no force of attraction towards the centre and its our inertia forcing us to stay at a point as once gravity had acted on the object
why should it exist .. i mean its all an assumption and the evidences are empirical
We have equations to prove it and lies of evidence to support. we orbit because we have a velocity and the sun is pulling us. Gravity is a law, we know it exists.
yeah sure there are equations but they are based on observations and assumptions
g is obtained by a simple pendulum experiment ...
gravity is tested by dropping a rock...
and also there were so many newtonian laws proved wrong by einstein . jus saying that its a law doesnt mean it cant be wrong
pendulum is good for showing energy transfer, here is an article on the detection of gravitational waves: ***ligo.org/detections.php
yeah but g is calculated by pendulum oscillations ..
thats what .. einstein s fabric model explains that force of attraction by sun on earth but i am talking about force of attraction by earth on objects on earth
no... this is how gravity is calculated:F = G*((m sub 1*m sub 2)/r^2)
gravitational constant is obtained EXPERIMENTALLY
the G part
Calculate the time of one oscillation or the period (T) by dividing the total time by the number of oscillations you counted. Use your calculated (T) along with the exact length of the pendulum (L) in the above formula to find "g." This is your measured value for "g."
G is the universal gravitational constant. F is the gravity
search up the gravity equation
yeahh G is obtained experimentally
sure yes
thats what .. after all its EXPERIMENTALLY calculated so its empirical
yes... so where do we disagree?
its empirical whixh means it can be proved wrong
so cant just say why wouldnt gravity exists
the constant, sure but extremely unlikely it is wrong. gravity however exists, there are equations and loads of support surrounding the concept. unfortunately I don't have a high enough background in physics but have this discussion with a physicist
can u suggest a platform where i can?
stack overflow
stack exchange, physics section***
its an app?
there is! it is also a website as well
nice talking to you
likewise :)
What is the percentage by massof oxygen in Al2(so4)3
Isiguzo Reply
A spring with 50g mass suspended from it,has its length extended by 7.8cm 1.1 determine the spring constant? 1.2 it is observed that the length of the spring decreases by 4.7cm,from its original length, when a toy is place on top of it. what is the mass of the toy?
Silindelo Reply
solution mass = 50g= 0.05kg force= 50 x 10= 500N extension= 7.8cm = 0.078m using the formula Force= Ke K = force/extension 500/.078 = 6410.25N/m
1.2 Decrease in length= -4.7cm =-0.047m mass=? acceleration due to gravity= 10 force = K x e force= mass x acceleration m x a = K x e mass = K x e/acceleration = 6410.25 x 0.047/10 = 30.13kg
1.1 6.28Nm-¹
1.2 0.03kg or 30g
I used g=9.8ms-²
you should explain how yoy got the answer Anita
with the fomular F=mg I got the value for force because now the force acting on the spring is the weight of the object and also you have to convert from grams to kilograms and cm to meter
so the spring constant K=F/e where F is force and e is extension
In this first example why didn't we use P=P° + ¶hg where ¶ is density
Anita Reply
Density = force applied x area p=fA =p = mga, then a=h therefore substitute =p =mgh
Please correct me
sorry I had a little typo in my question
Density = m/v (mass/volume) simple as that
Hlehle vilakazi how density is equal to force * area and you also wrote p= mgh which is machenical potential energy ? how ?
what is wave
Alfred Reply
who can state the third equation of motion
wave is a distrubance that travelled in medium from one point to another with carry energy .
wave is a periodic disturbance that carries energy from one medium to another..
what exactly is a transverse wave then?
two particles rotate in a rigid body then acceleration will be ?
kinza Reply
same acceleration for all particles because all prticles will be moving with same angular velocity.so at any time interval u find same acceleration of all the prticles
what is electromagnetism
David Reply
It is the study of the electromagnetic force, one of the four fundamental forces of nature. ... It includes the electric force, which pushes all charged particles, and the magnetic force, which only pushes moving charges.
what is units?
Subhajit Reply
units as in how
What is th formular for force
Joseph Reply
F = m x a
State newton's second law of motion
Seth Reply
can u tell me I cant remember
force is equal to mass times acceleration
The acceleration of a system is directly proportional to the and in the same direction as the external force acting on the system and inversely proportional to its mass that is f=ma
The rate of change of momentum of a body is directly proportional to the force exerted on that body.
The uniform seesaw shown below is balanced on a fulcrum located 3.0 m from the left end. The smaller boy on the right has a mass of 40 kg and the bigger boy on the left has a mass 80 kg. What is the mass of the board?
Asad Reply
Consider a wave produced on a stretched spring by holding one end and shaking it up and down. Does the wavelength depend on the distance you move your hand up and down?
Sohail Reply
no, only the frequency and the material of the spring
how to read physics ncert?
beat line read important. line under line
Practice Key Terms 8

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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