<< 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

Prove that 1/d+1/v=1/f
James Reply
What interference
Moyinoluwa Reply
What is a polarized light called?
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
what is radioactive element
Half of the total time required by a radioactive nuclear atom to totally disintegrate
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
state the laws of refraction
state laws of reflection
Why does a bicycle rider bends towards the corner when is turning?
When do we say that the stone thrown vertically up wards accelerate negatively?
Give two importance of insulator placed between plates of a capacitor.
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.
when was the name taken from
Biola Reply
retardation of a car
when was the name retardation taken
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
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.
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
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
is not just a material
it is the surface of a metal
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
an atom is the smallest particle of a element which can take part in chemical reaction.
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
pls what is mirage
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
what is the dimensional formula for torque
Otto Reply
same units of energy
what is same units of energy?
M L2 T -2
it is like checking the dimension of force. which is ML2T-2
M L2 T-2
what is the significance of moment of inertia?
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?