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Changing intensity levels of a sound

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


We 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. We can solve this problem by 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 .

    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.

    Note that
    log 10 b log 10 a = log 10 ( b a ) .
  2. Use the definition of β to obtain
    β 2 β 1 = 10 log 10 ( I 2 I 1 ) = 10 log 10 2.00 = 10 ( 0.301 ) dB .

    β 2 β 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.

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Check Your Understanding Identify common sounds at the levels of 10 dB, 50 dB, and 100 dB.

10 dB: rustle of leaves; 50 dB: average office; 100 dB: noisy factory

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Another decibel scale is also 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 this text 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.

Hearing and pitch

The human ear has a tremendous range and sensitivity. It can give us a wealth of simple information—such as pitch, loudness, and direction.

The perception of frequency is called pitch    . Typically, humans have excellent relative pitch and can discriminate between two sounds if their frequencies differ by 0.3% or more. For example, 500.0 and 501.5 Hz are noticeably different. Musical notes    are sounds of a particular frequency that can be produced by most instruments and in Western music have particular names, such as A-sharp, C, or E-flat.

The perception of intensity is called loudness    . At a given frequency, it is possible to discern differences of about 1 dB, and a change of 3 dB is easily noticed. But loudness is not related to intensity alone. Frequency has a major effect on how loud a sound seems. Sounds near the high- and low-frequency extremes of the hearing range seem even less loud, because the ear is less sensitive at those frequencies. When a violin plays middle C, there is no mistaking it for a piano playing the same note. The reason is that each instrument produces a distinctive set of frequencies and intensities. We call our perception of these combinations of frequencies and intensities tone quality or, more commonly, the timbre    of the sound. Timbre is the shape of the wave that arises from the many reflections, resonances, and superposition in an instrument.

Questions & Answers

who discover periodic table?
lovet Reply
it wasn't discovered , it was made.and the person who made it was dmitri mendeleev. dobreinier and newland gave their laws before dmitri related periodic table but wasn't successful in their work
Nope, numerous number of scientist had actually contributed in the making of periodic table. Dmitri Mendeleev succeeded making all the elements into the right order in accordance to their atomic number.
what is the Greek name for calcium
Oniyide Reply
different types of wave
Yog Reply
longitudinal and transverse waves
a gun is kept in the state that it cannot move anywhere and the bullet is fired. Then what is the effect on the velocity of bullet and KE of gun ?
Gobinda Reply
want is meant by the term solar system
jafar Reply
it refers to the sun and all heavenly bodies revolving around it.
excatly...for sure
in addition to Danie's, a solar system is a collection of planets and their moons, asteroids, and other objects bound together by the Star's gravitational force directly or indirectly.
what is meant by total internal reflection
Akshay Reply
what iw meant by total internal reflection
Lorentz force?
study fibre optics. .you will get total internal reflection
what is Lorentz force?
a ray of light traveling at an angle of incidence greater than critical angle from denser to rarer medium is totally reflected back into the denser medium is called total internal reflaction
motion in strat line where is this chapter
Vijaybhai Reply
motion in straight line is kinematic's part
this defination isn't correct
motion in one dimension
what is Lorentz force?
jyotirmayee Reply
what is maxwell electromagnetic law?
at what angle should the two forces 2p and root 2p acts so that the resultant force is p root 10
Akshay Reply
what answer fir this
what's the working difference between a dynamo and a pump?
Piyali Reply
a dynamo is basically a dc generator while pump is usually equipped with a motor
a dynamo converts mechanical energy to electrical while a pump is opposite to that
why sea water looks bluish?
Piyali Reply
cuz the sky is blue...
you see the reflexion of the "blue" sky in the water
somewhere sea water turns green why?
never seen bro... are u sure ?
ur answer was correct but due to the presence of phytoplankton color can be changed near the shore
waaaww... you re awesome
because of the reflection of the sky
rays coming from the sun consist of all 7 colours ie.VIBGYOR. when the ray strikes surface of water,all colors gets absorbed by it except blue which gets reflected by it.so we find the sea water appearing bluish
how can someone identify sea water from rain water
i think it's not possible as because rainwater consists of water from all kind of water bodies ie.lakes,seas etc but u can predict if u have a sea nearby ur home or city
i need solutions of unuversity pbysucs volume 1
Vimla Reply
me too
Help us if anyone knows
bring questions
actually if u wanted whole book solution then u should buy the solution book
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what is three dimensional coordinate system?
Sachindra Reply
considering the change of vectors in all three dimensions of space
direction co-sign of vector questions
Vipin Reply
opposite mean
what is the different between action and reaction?
Asali Reply
action is external force. Reaction exists because of the external action. Reaction is mostly an internal force
The difference is said in the word itself. There is no existance of reaction without an application of action. So action occur first then reaction. Reaction may produce in body itself or to other body i.e., it may be internal or external.
or we can say , reaction is the result of action
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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