ACOUSTICS 1ACOUSTICS 1

INTRODUCTION TO ACOUSTICSINTRODUCTION TO ACOUSTICS

SOUND ENERGY is electromagnetic energy of a SOUND ENERGY is electromagnetic energy of a very low frequency compared to radio, television, very low frequency compared to radio, television, and light energy.and light energy.

Sound energy is physical energy that requires a Sound energy is physical energy that requires a medium in which to travel – the energy is medium in which to travel – the energy is transferred by a continual bounce of one transferred by a continual bounce of one molecule of the medium against another.molecule of the medium against another.

Sound energy travels through an elastic medium Sound energy travels through an elastic medium such as air and solids, and through water, such as air and solids, and through water, emanating from its source in a spherical direction emanating from its source in a spherical direction outward – much as a burst of light spreads from outward – much as a burst of light spreads from its source.its source.

This physical energy travels until all motion is This physical energy travels until all motion is absorbed into the elasticity of the medium, and absorbed into the elasticity of the medium, and the energy decays. the energy decays.

The The physical energy of sound is not audible until it physical energy of sound is not audible until it strikes a mechanism that has the capability of strikes a mechanism that has the capability of transforming physical energy into an transforming physical energy into an audible sensationaudible sensation..

If a light fixture were to fall from the ceiling in an If a light fixture were to fall from the ceiling in an empty room, and no one is present to hear the results, empty room, and no one is present to hear the results, the impact that would cause sound energy is not the impact that would cause sound energy is not transformed into audibility – so no “sound” as we know transformed into audibility – so no “sound” as we know it is present – only untransformed sound energy.it is present – only untransformed sound energy.

So So physical sound energy is not ‘sound’ until audibility physical sound energy is not ‘sound’ until audibility happenshappens. .

Compare that concept to what you know as radio Compare that concept to what you know as radio waves, which is electromagnetic energy of much higher waves, which is electromagnetic energy of much higher frequency. It is not physical energy and does not frequency. It is not physical energy and does not require a medium through which to travel. But it does require a medium through which to travel. But it does require a mechanism to reveal its message. You and I require a mechanism to reveal its message. You and I would agree that in this room, one could turn on an AM would agree that in this room, one could turn on an AM or FM radio, or a television set, and sounds could be or FM radio, or a television set, and sounds could be heard – heard – which is to say the energy is present, but not which is to say the energy is present, but not audible without an amplifier to transform the energy audible without an amplifier to transform the energy into physical energy – which is in turn changed to into physical energy – which is in turn changed to audible sensations by the human ear.audible sensations by the human ear.

Consider also, the types of medium that transfer Consider also, the types of medium that transfer energy well, and those that do not. If a material energy well, and those that do not. If a material is highly “elastic” there is activity within the is highly “elastic” there is activity within the molecules when subjected to physical energy. molecules when subjected to physical energy. Such Such materials as wood, steel, water, and air are materials as wood, steel, water, and air are elastic materials, and transport energy wellelastic materials, and transport energy well..

But a But a soft material such as insulation, or brittle soft material such as insulation, or brittle materials such as concrete and masonry are not materials such as concrete and masonry are not as elastic and do not transport energy wellas elastic and do not transport energy well. But . But such materials are useful as sound attenuation – such materials are useful as sound attenuation – when it is desirable to limit the transfer of sound when it is desirable to limit the transfer of sound energy. energy.

Construction materials that have been Construction materials that have been acoustically tested are assigned a acoustically tested are assigned a Noise Noise Reduction CoefficientReduction Coefficient, which indicates the degree , which indicates the degree to which the material reflects or absorbs sound to which the material reflects or absorbs sound energy. Materials that have a rating of more than energy. Materials that have a rating of more than 20% are absorptive and less than 20% are 20% are absorptive and less than 20% are reflective. reflective. Absorptive materials do not transfer Absorptive materials do not transfer sound wellsound well. .

CHARACTERISTICS OF SOUND ENERGYCHARACTERISTICS OF SOUND ENERGY

Sound energy is characterized in two ways; Sound energy is characterized in two ways; One, by One, by pitchpitch, which is the frequency with which the , which is the frequency with which the energy vibrates the medium through which it travels.energy vibrates the medium through which it travels.Two, by Two, by loudnessloudness, which is the intensity strength of , which is the intensity strength of the source of the energy to cause the vibrations. the source of the energy to cause the vibrations.

The pitch of a sound is the number of times it The pitch of a sound is the number of times it vibrates in cycles over a period of timevibrates in cycles over a period of time, such as , such as cycles per second, or Hertz. cycles per second, or Hertz.

Sounds with low frequency are low in audibility, such Sounds with low frequency are low in audibility, such as a bass horn, or the left end of a piano. The C note as a bass horn, or the left end of a piano. The C note two octaves left of middle C has a frequency of 65 two octaves left of middle C has a frequency of 65 hertz. Middle C has a frequency of 256 hertz.hertz. Middle C has a frequency of 256 hertz.Sounds with a high frequency are high in audibility, Sounds with a high frequency are high in audibility, such as a flute or the right end of the piano. The C such as a flute or the right end of the piano. The C note two octaves to right of middle C has a frequency note two octaves to right of middle C has a frequency of 1035 hertz.of 1035 hertz.

Consider that the difference in AM radio, FM, radio, Consider that the difference in AM radio, FM, radio, Television, and Aircraft Transmission is simply a Television, and Aircraft Transmission is simply a difference in the pitch of the sound energy.difference in the pitch of the sound energy.

AM radio is assigned a frequency between 540 and AM radio is assigned a frequency between 540 and 1600 1600 thousandthousand cycles per second, or kilohertz. cycles per second, or kilohertz.

FM radio is assigned a frequency between 88 and FM radio is assigned a frequency between 88 and 112 112 millionmillion cycles per second, or megahertz. cycles per second, or megahertz.

Television is a notch or two higher than that, and Television is a notch or two higher than that, and commercial aircraft transmission higher than commercial aircraft transmission higher than television.television.

The reason physical sound energy will not travel to The reason physical sound energy will not travel to outer space is the absence of a medium, however outer space is the absence of a medium, however since the higher electronic frequencies do not need since the higher electronic frequencies do not need a medium, earth can communicate with orbiting a medium, earth can communicate with orbiting satellites, the Mars and Saturn expeditions – or the satellites, the Mars and Saturn expeditions – or the tiny little weird looking guys with large heads and tiny little weird looking guys with large heads and long fingers. long fingers.

LOUDESS OF PHYSICAL SOUND ENERGYLOUDESS OF PHYSICAL SOUND ENERGY is the is the amount of pressure the energy places on the amount of pressure the energy places on the particles of the medium through which it travels. particles of the medium through which it travels. The strength of the energy determines how far the The strength of the energy determines how far the medium will be vibrated.medium will be vibrated.

Were I to stand on the steps of the Administration Were I to stand on the steps of the Administration Building and shout, I could not be heard at the Building and shout, I could not be heard at the entrance of the Architecture Building because my entrance of the Architecture Building because my voice could not generate enough energy for the voice could not generate enough energy for the human ear to sense audibility.human ear to sense audibility.

Loudness is measured in units of Loudness is measured in units of DecibelsDecibels, on a , on a scale where zero is considered the threshold of scale where zero is considered the threshold of hearing for a healthy human – barely audible.hearing for a healthy human – barely audible.

At the high end of audibility on the decibel scale, At the high end of audibility on the decibel scale, very loud sounds such as 130 decibels is considered very loud sounds such as 130 decibels is considered the threshold of pain – because the energy that the threshold of pain – because the energy that vibrates the medium also affects the physical parts vibrates the medium also affects the physical parts of the human ear. of the human ear.

Normal human conversational voice loudness is 20 Normal human conversational voice loudness is 20 to 40 decibels.to 40 decibels.

\\ THE RELATIONSHIP OF LOUDNESS TO PHYSICAL SOUND THE RELATIONSHIP OF LOUDNESS TO PHYSICAL SOUND

ENERGYENERGY

Let Let I.E.I.E. represent represent intensity energyintensity energy, the level of sound , the level of sound energy expressed in units of energy expressed in units of watts per square watts per square centimetercentimeter..

Let Let I.L.I.L. represent represent intensity loudnessintensity loudness, the measurable , the measurable quantity of audibility at the point of hearing, in decibels.quantity of audibility at the point of hearing, in decibels.

LetLet I I00 represent represent the amount of intensity energy that will the amount of intensity energy that will make the least audible soundmake the least audible sound to the human ear. This is to the human ear. This is a constant, and the value is 10a constant, and the value is 10-16-16 watts per square watts per square centimetercentimeter

The mathematical relationship is:The mathematical relationship is:

Intensity LoudnessIntensity Loudness = 10 logarithm = 10 logarithm1010 [ [ Intensity EnergyIntensity Energy / / II0 0 ]]

OrOr ILIL = 10 log = 10 log IEIE / / 1010-16-16

So one could say that the loudness of a sound, So one could say that the loudness of a sound, measured in Bells, is the logarithm (to the base 10) measured in Bells, is the logarithm (to the base 10) of the ratio of the amount of energy available to of the ratio of the amount of energy available to make the sound, to that energy required for the make the sound, to that energy required for the threshold of hearing. threshold of hearing.

And since there are 10 bels in a deci-bel, the And since there are 10 bels in a deci-bel, the function is multiplied by 10 to get units of decibels. function is multiplied by 10 to get units of decibels.

In the solution of problems dealing with sound, In the solution of problems dealing with sound, mathematical calculations utilizing LOGARITHMS mathematical calculations utilizing LOGARITHMS will be used, simply because of the immense range will be used, simply because of the immense range of numbers from extremely large to extremely of numbers from extremely large to extremely small. small.

Logarithms to the base 10 will be used. If you have Logarithms to the base 10 will be used. If you have an electronic calculator, it probably has a function an electronic calculator, it probably has a function “log,” which are logarithms to the base 10. A base “log,” which are logarithms to the base 10. A base of 10 allows easy manipulation of large numbers, of 10 allows easy manipulation of large numbers, using exponents for simplicity. using exponents for simplicity.

WHY LOG, OR LOGARITHMS ?WHY LOG, OR LOGARITHMS ?The use of logarithms is a mathematical The use of logarithms is a mathematical

process in which accurate results can be process in which accurate results can be obtained when extremely large or small numbers obtained when extremely large or small numbers are involved. Your electronic calculator probably are involved. Your electronic calculator probably has the ‘log’ button on it, which is log to the base has the ‘log’ button on it, which is log to the base 10. Forget the ‘ln’ button, as that is log to the 10. Forget the ‘ln’ button, as that is log to the base ‘e’. All acoustics problems will utilize base ‘e’. All acoustics problems will utilize logarithms to the base 10.logarithms to the base 10.

As a demonstration as to how logs work As a demonstration as to how logs work involving multiplication and division refer to your involving multiplication and division refer to your handout. Logarithms can be done to ANY base handout. Logarithms can be done to ANY base number, number, but logs to base 10 is our standard but logs to base 10 is our standard because it involves multiple zeros.because it involves multiple zeros.

In early times before electronic calculators, In early times before electronic calculators, logarithms were used to accurately calculate logarithms were used to accurately calculate extremely large or small numbers.extremely large or small numbers.

For instance, a land area that is “X” wide by “Y” For instance, a land area that is “X” wide by “Y” long equals “Z” square feet. Easy and quick to long equals “Z” square feet. Easy and quick to do with a calculator.do with a calculator.

But before calculators, logarithmic tables were But before calculators, logarithmic tables were available to do the calculation a little easier than available to do the calculation a little easier than long multiplication.long multiplication.

Log “X” = an X numberLog “X” = an X numberLog “Y” = a Y number Log “Y” = a Y number add the numbers add the numbers

together to together to get a Z get a Z number number

Take the anti-log of the Z number and get the Take the anti-log of the Z number and get the “Z” quantity in square feet.“Z” quantity in square feet.

Illustration:Illustration:

You know that 10You know that 1044 power = 10,000 power = 10,000

In your calculator, enter 10,000. Then press log and In your calculator, enter 10,000. Then press log and get 4get 4

so the logarithm of 10,000 = 4 . . . Which is the so the logarithm of 10,000 = 4 . . . Which is the exponent to which 10 must be raised to get a given exponent to which 10 must be raised to get a given number.number.

Now with 4 in your calculator, press 10Now with 4 in your calculator, press 10xx and get and get 10,00010,000

So the antilogarithm of 4 = 10,000So the antilogarithm of 4 = 10,000

All of which means, if you don’t already know this, All of which means, if you don’t already know this, and you don’t practice the exercise, you will never and you don’t practice the exercise, you will never get it.get it.

The solution of acoustics problems involves not The solution of acoustics problems involves not only logarithms, but a basic understanding of only logarithms, but a basic understanding of transposing basic mathematical functions.transposing basic mathematical functions.

When the upper part of a fraction is taken across When the upper part of a fraction is taken across the equal sign, that part goes to the bottom of the equal sign, that part goes to the bottom of the fraction line, without changing the value of the fraction line, without changing the value of the equation;the equation;

AA / B = C / D transposed 1 / B = C / / B = C / D transposed 1 / B = C / AADD

Consequently when the bottom part of a fraction Consequently when the bottom part of a fraction is taken across the equal sign it goes to the top is taken across the equal sign it goes to the top of the fraction line, without changing the value of of the fraction line, without changing the value of the equation.the equation.

A / A / BB = C / D transposed A = = C / D transposed A = BBC / DC / D

When a number is transferred to the other side of When a number is transferred to the other side of the equal sign, the sign of the number is the equal sign, the sign of the number is changed.changed.

AB AB + CD+ CD = XYZ transferred AB = XYZ = XYZ transferred AB = XYZ - CD- CDor ABor AB – CD – CD = XYZ transferred AB = XYZ= XYZ transferred AB = XYZ + CD + CD

If the bottom number of a fraction has an If the bottom number of a fraction has an exponent, and the number is moved to the top of exponent, and the number is moved to the top of the fraction line, the sign of the exponent the fraction line, the sign of the exponent changes.changes.

AB = CD / AB = CD / EE-4-4 transferred AB = CD x transferred AB = CD x EE+4+4

OR ABC = 10 log [ DEF / OR ABC = 10 log [ DEF / 10 10 -16-16 ] transferred = ] transferred =

ABC = 10 log [ DEF x ABC = 10 log [ DEF x 10 10 +16+16 ] ] When numbers with exponents are to be When numbers with exponents are to be

multipliedmultiplied, the , the exponents exponents algebraicallyalgebraically add. add.

It is essential for clarity of understanding the It is essential for clarity of understanding the steps involved in solutions to acoustic problems steps involved in solutions to acoustic problems to keep numbers as small as possible.to keep numbers as small as possible.

With sophisticated electronic calculators today, it With sophisticated electronic calculators today, it is easy to put numbers into a complex formula is easy to put numbers into a complex formula and let the calculator grind and click through and let the calculator grind and click through several steps to a solution, coughing out an several steps to a solution, coughing out an answer – and likely the operator has no clue as to answer – and likely the operator has no clue as to the direction of the wayward functions if the the direction of the wayward functions if the wrong answer emerges.wrong answer emerges.

Do yourself a favor – do it step by step, and Do yourself a favor – do it step by step, and where possible, reduce complex numbers to a where possible, reduce complex numbers to a number between one and ten by using exponents number between one and ten by using exponents – then solve the equations. – then solve the equations.

The use of smaller numbers make it easier The use of smaller numbers make it easier to visualize to visualize reasonable solutions. reasonable solutions.

SOUND PROJECTIONSOUND PROJECTION

1 1 DIRECTION OF SOUND ENERGY DIRECTION OF SOUND ENERGY

Physically emanates spherically in all Physically emanates spherically in all directions.directions.

Movement is resisted by the density and Movement is resisted by the density and elasticity of the medium through which it elasticity of the medium through which it travels . . . SOtravels . . . SO

A relation exists between the AMOUNT of A relation exists between the AMOUNT of physical sound energy and the DISTANCE it physical sound energy and the DISTANCE it travels.travels.

22 THE INVERSE SQUARE LAWTHE INVERSE SQUARE LAW is very is very much the same rule realized in much the same rule realized in illumination data; that light energy is illumination data; that light energy is diminished proportionately a distance diminished proportionately a distance from the source. And so is sound energy.from the source. And so is sound energy.

Refer to supplementary material, “Basic Refer to supplementary material, “Basic Theory”, Inverse Square Law, top of page. Theory”, Inverse Square Law, top of page. A diagram represents the movement of A diagram represents the movement of sound energy from a source. Two areas sound energy from a source. Two areas and two distances are illustrated.and two distances are illustrated.

Observe in the diagram, the letter ‘I’ is Observe in the diagram, the letter ‘I’ is labeled sound intensity. For clarity, we will labeled sound intensity. For clarity, we will use the designation IE for “INTENSITY use the designation IE for “INTENSITY ENERGY” to distinguish from “INTENSITY ENERGY” to distinguish from “INTENSITY LOUDNESS.”LOUDNESS.”

The law states that the amount of sound The law states that the amount of sound energy at any point is inversely proportional energy at any point is inversely proportional to the square of the distance from the point to the square of the distance from the point of source. Mathematically it becomes,of source. Mathematically it becomes,

IEIE11 // IE IE22 = [= [ d d22 / / dd11 ]]22

The formula is useful to determine the The formula is useful to determine the amount of sound energy at a point when the amount of sound energy at a point when the quantity of sound energy is known at quantity of sound energy is known at another point, and relative distances are another point, and relative distances are known.known.

Imagine two points where sound Imagine two points where sound energy is measured, energy is measured, one point located a one point located a certain distance from the sourcecertain distance from the source, and , and the the other point a distance from the source other point a distance from the source that is two times that of the firstthat is two times that of the first. The . The amount of energy at the second point is amount of energy at the second point is only only one-fourth the value of the energy at one-fourth the value of the energy at the first pointthe first point..

But remember the relationship of But remember the relationship of Loudness to Energy, and realize Loudness to Energy, and realize

. . . The inverse square law pertains ONLY . . . The inverse square law pertains ONLY to to Intensity ENERGYIntensity ENERGY. Intensity Energy is . Intensity Energy is directly accumulative when multiple directly accumulative when multiple sound sources are present, sound sources are present, but Intensity but Intensity Loudness IS NOT.Loudness IS NOT.

Two useful formulas evolve; the relationship Two useful formulas evolve; the relationship ofof loudness to energy loudness to energy, and the relationship of, and the relationship of energy to distances energy to distances through which energy through which energy travels in a medium. travels in a medium.

IL IL = 10 log= 10 log IEIE / 10/ 10-16-16 ( (Loudness to EnergyLoudness to Energy))

IEIE1 1 // IE IE22 = [= [ dd22 // dd11 ]]2 2 ((Energy to DistanceEnergy to Distance))

If an Intensity If an Intensity LOUDNESSLOUDNESS is known, the is known, the ENERGYENERGY required to make that loudness can be found.required to make that loudness can be found.

If an If an ENERGYENERGY is known, the Intensity is known, the Intensity LOUDNESS LOUDNESS the energy will cause, can be found.the energy will cause, can be found.

If an energy at a stated distance is known, If an energy at a stated distance is known, energy from the same source at another energy from the same source at another distance can be found. distance can be found.

3 3 EXAMPLE PROBLEM ONEEXAMPLE PROBLEM ONE– DETERMINE – DETERMINE LOUDNESS AT A GIVEN POINT . . . If LOUDNESS AT A GIVEN POINT . . . If loudness at one point is known:loudness at one point is known:

Say a horn with an Intensity Loudness Say a horn with an Intensity Loudness equals 60 decibels at a distance of 12 feet equals 60 decibels at a distance of 12 feet from the horn. Find the Intensity from the horn. Find the Intensity Loudness at a distance of 84 feet from the Loudness at a distance of 84 feet from the horn.horn.

Solution: First, find the amount of Solution: First, find the amount of Intensity Energy that caused the 60 Intensity Energy that caused the 60 decibels at a distance 12 feet from the decibels at a distance 12 feet from the horn:horn:

ILIL1212 = 10 log [IE = 10 log [IE1212 / 10 / 10-16-16]] ; ;

6060 = 10 log [ IE= 10 log [ IE12 12 / 10 / 10 -16-16 ] ]

Divide both sides of the equation by 10 to Divide both sides of the equation by 10 to make smaller numbers:make smaller numbers:

6 = log [ IE6 = log [ IE12 12 / 10 / 10 -16-16 ] ]

To solve the equation: since you can’t take To solve the equation: since you can’t take the logarithm of the unknown quantity, IEthe logarithm of the unknown quantity, IE12, 12,

then take the then take the ANTI-logarithmANTI-logarithm of both sides . of both sides . . .. .

. . . To get rid of the function, “log”. . . To get rid of the function, “log”

And what is the anti-logarithm of 6 ? And what is the anti-logarithm of 6 ? Using logarithms to the base 10, the anti-Using logarithms to the base 10, the anti-log of 6 is 10log of 6 is 1066

With your calculator find anti-log of 6. It With your calculator find anti-log of 6. It may be identified on your calculator may be identified on your calculator button as 10 button as 10 x power x power

101066 = 1,000,000 = 1,000,000

So put 1,000,000 in your calculator and So put 1,000,000 in your calculator and punch ‘LOG’.punch ‘LOG’.

The answer is six.The answer is six.

And what is the And what is the ANTI logANTI log of the of the expression expression

log [ IElog [ IE12 12 / 10 / 10 -16-16 ] ]

It is simply It is simply IE IE12 12 / 10 / 10 -16-16 So, So,

101066 = = IEIE12 12 / 10 / 10 -16-16 , and IE , and IE12 12 = 10= 1066 x x 10 10 --

1616

IEIE12 12 == 10 10 -10-10 watts per sq.cm. watts per sq.cm.

the amount of energy to make the 60 decibelsthe amount of energy to make the 60 decibels

Next, with the inverse square formula, find Next, with the inverse square formula, find the amount of energy available at a distance the amount of energy available at a distance of 84’:of 84’:

IEIE12 12 // IE IE8484 = [= [ dd8484 // dd1212 ]]2 2

10 10 -10-10 = 84 = 84 2 2 = 49 10 = 49 10 -10-10 = = IEIE8484

IEIE84 84 12 4912 49

IEIE84 84 = 1 x 10 = 1 x 10 -10-10 = .0204 x 10 = .0204 x 10 -10-10 4949

IEIE84 84 = 2.04 x 10= 2.04 x 10-2-2 x 10 x 10 -10-10 = = 2.04 x 10 2.04 x 10 -12-12

The amount of energy available at a distance The amount of energy available at a distance of 84’of 84’

Finally, Finally, find the sound made at a distance of find the sound made at a distance of

84’84’ : :

ILIL8484 = 10 log= 10 log IEIE8484 / 10/ 10-16-16 = 10 log= 10 log 2.04 x 10 2.04 x 10 -12-12

1010-16-16

ILIL8484 = 10 log= 10 log x x 2.04 x 10 2.04 x 10 -12 -12 xx 1010+16+16

ILIL8484 = 10 log= 10 log x x 2.04 2.04 x x 1010+4+4

loglog 2.04 = .3096 ; 2.04 = .3096 ; log 10log 10+4 +4 = 4 ; = 4 ; add them together soadd them together so loglog x x 2.04 2.04 x x 1010+4 +4 = 4.3096 ; and= 4.3096 ; and

ILIL84 84 = 10 x 4.3096 = = 10 x 4.3096 = 43.096 decibels at 84 43.096 decibels at 84 ft.ft.

**

PRACTICE PROBLEM ONE:PRACTICE PROBLEM ONE: In this classroom, say I am standing 12 feet from In this classroom, say I am standing 12 feet from

a certain student who consistently hears my a certain student who consistently hears my voice at 30 decibels. How loud is my voice 36 feet voice at 30 decibels. How loud is my voice 36 feet away to a person on the back row?away to a person on the back row?

Solution: Solution: A) first find the Intensity Energy at 12 A) first find the Intensity Energy at 12 feetfeet, then , then B) by the inverse square law, find the B) by the inverse square law, find the energy available at 36 feetenergy available at 36 feet, then , then C) with the C) with the loudness formula, find the Intensity Loudness at loudness formula, find the Intensity Loudness at 36 feet.36 feet.

PRACTICE PROBLEM TWOPRACTICE PROBLEM TWO sound from multiple sound from multiple sources. Since loudness is dependent upon the sources. Since loudness is dependent upon the intensity energy created, in determining the intensity energy created, in determining the loudness of multiple sounds, find the intensity loudness of multiple sounds, find the intensity energy of each source, then add them for the energy of each source, then add them for the total sum of Intensity Energy.total sum of Intensity Energy.

Then from the Intensity Loudness formula, find Then from the Intensity Loudness formula, find the total sound Intensity. Say the loudness of the total sound Intensity. Say the loudness of one trombone is 40 decibels. How loud would 76 one trombone is 40 decibels. How loud would 76 trombones be, playing simultaneously, each as trombones be, playing simultaneously, each as the same frequency and loudness, each the same frequency and loudness, each producing identical energy?producing identical energy?

PRACTICE PROBLEM THREE:PRACTICE PROBLEM THREE:

A train engine sounds its horn 150’ away from A train engine sounds its horn 150’ away from a person, who hears the sound at 70 decibels.a person, who hears the sound at 70 decibels. As As the train moves closer, at 30’ from the person, it the train moves closer, at 30’ from the person, it sounds the horn again.sounds the horn again.

At what Intensity Loudness does the person hear At what Intensity Loudness does the person hear the second horn?the second horn?