<< Chapter < Page Chapter >> Page >
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

Calculating sound intensity levels: sound waves

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


We are given Δ p size 12{Δp} {} , so we can calculate I using the equation I = ( Δ p ) 2 / ( 2 pv w ) 2 . Using I , we can calculate β straight from its definition in β dB = 10 log 10 ( I / I 0 ) .


(1) Identify knowns:

Sound travels at 331 m/s in air at 0ºC .

Air has a density of 1.29 kg /m 3 at atmospheric pressure and 0ºC .

(2) Enter these values and the pressure amplitude into I = ( Δ p ) 2 / ( 2 ρv w ) :

I = ( Δ p ) 2 2 ρv w = 0.656 Pa 2 2 1 . 29 kg/m 3 331 m/s = 5 . 04 × 10 4 W/m 2 . size 12{I= { { left (Δp right ) rSup { size 8{2} } } over {2 ital "pv" size 8{m}} } = { { left (0 "." "656"" Pa" right ) rSup { size 8{2} } } over {2 left (1 "." "29"" kg/m" rSup { size 8{3} } right ) left ("331"" m/s" right )} } =5 "." "04" times "10" rSup { size 8{ - 4} } " W/m" rSup { size 8{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.

Got questions? Get instant answers now!

Change intensity levels of a sound: what happens to the decibel level?

Show that if one sound is twice as intense as another, it has a sound level about 3 dB higher.


You are given that the ratio of two intensities is 2 to 1, and are then asked to find the difference in their sound levels in decibels. You can solve this problem using of the properties of logarithms.


(1) Identify knowns:

The ratio of the two intensities is 2 to 1, or:

I 2 I 1 = 2 . 00 . size 12{ { {I rSub { size 8{2} } } over {I rSub { size 8{1} } } } =2 "." "00"} {}

We wish to show that the difference in sound levels is about 3 dB. That is, we want to show:

β 2 β 1 = 3 dB . size 12{β rSub { size 8{2} } - β rSub { size 8{1} } =3" dB"} {}

Note that:

log 10 b log 10 a = log 10 b a . size 12{"log" rSub { size 8{"10"} } b - "log" rSub { size 8{"10"} } a="log" rSub { size 8{"10"} } left ( { {b} over {a} } right ) "." } {}

(2) Use the definition of β to get:

β 2 β 1 = 10 log 10 I 2 I 1 = 10 log 10 2.00 = 10 0 . 301 dB . size 12{β rSub { size 8{2} } - β rSub { size 8{1} } ="10 log" rSub { size 8{"10"} } left ( { {I rSub { size 8{2} } } over {I rSub { size 8{1} } } } right )="10"" log" rSub { size 8{"10"} } 2 "." "00"="10" "." left (0 "." "301" right )"dB"} {}


β 2 β 1 = 3 .01 dB . size 12{β rSub { size 8{2} } - β rSub { size 8{1} } =3 "." "01"" dB"} {}


This means that the two sound intensity levels differ by 3.01 dB, or about 3 dB, as advertised. Note that because only the ratio I 2 / I 1 is given (and not the actual intensities), this result is true for any intensities that differ by a factor of two. For example, a 56.0 dB sound is twice as intense as a 53.0 dB sound, a 97.0 dB sound is half as intense as a 100 dB sound, and so on.

Got questions? Get instant answers now!

It should be noted at this point that there is another decibel scale in use, called the sound pressure level    , based on the ratio of the pressure amplitude to a reference pressure. This scale is used particularly in applications where sound travels in water. It is beyond the scope of most introductory texts to treat this scale because it is not commonly used for sounds in air, but it is important to note that very different decibel levels may be encountered when sound pressure levels are quoted. For example, ocean noise pollution produced by ships may be as great as 200 dB expressed in the sound pressure level, where the more familiar sound intensity level we use here would be something under 140 dB for the same sound.

Take-home investigation: feeling sound

Find a CD player and a CD that has rock music. Place the player on a light table, insert the CD into the player, and start playing the CD. Place your hand gently on the table next to the speakers. Increase the volume and note the level when the table just begins to vibrate as the rock music plays. Increase the reading on the volume control until it doubles. What has happened to the vibrations?

Questions & Answers

what is heat
Ojo Reply
heat is the transfer of internal energy from one point to another
what is a wave
Williams Reply
wave means. A field of study
what are Atoms
is the movement back and front or up and down
how ?
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
an atom is the smallest unit( particle) of an element that bares it's chemical properties
what is electromagnetic induction?
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Larissa Reply
How do you convert 0.0045kgcm³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
Falana Reply
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Alright Thank you
Which one is the Bose-Einstein
can you explain what plasma and the I her one you mentioned
u can say sun or stars are just the state of plasma
but the are more than seven
list it out I wanna know
what the meaning of continuum
Akhigbe Reply
What state of matter is fire
Thapelo Reply
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Isn`t fire the plasma state of matter?
all this while I taught it was plasma
How can you define time?
Thapelo Reply
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
how can we define vector
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
what is the relativity of physics
Paul Reply
How do you convert 0.0045kgcm³ to the si unit?
What is the formula for motion
Anthony Reply
V=u+at V²=u²-2as
they are eqns of linear motion
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
Explain dopplers effect
Jennifer Reply
Not yet learnt
Explain motion with types
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Alabi Reply
Scalar quantity Because acceleration has only magnitude
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
its a scalar quantity
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
respect to prevailing force
What is the difference between impulse and momentum?
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
Or I = m(v-u)
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Calculation of kinetic and potential energy
dion Reply
K.e=mv² P.e=mgh
K is actually 1/2 mv^2
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
what is sound wave
Nworu Reply
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
its a longitudnal wave which is associted wth compresion nad rearfractions
what is power
it's also a capability to do something or act in a particular way.
Newton laws of motion
power also known as the rate of ability to do work
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
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?