Fundamentals of Sound

Fundamentals of Sound - Page 1

Noise Control Engineering

1

The Fundamentals

of Sound

Prepared by:

Dennis P. Driscoll, P.E.

Principal Consultant

Associates in Acoustics, Inc.

(303)670-9270

www.esion.com

The objective of this section is to provide a review of the fundamental definitions, terms, symbols and equations used in acoustics.



2

DEFINITION OF SOUND

A propagating disturbance through a physical medium, which becomes sound as we know it when detected by a microphone or listener.

The propagation sound wave is perceived by the ear as a pressure wave superimposed upon the ambient air pressure.

When you have a noise source, it puts energy into the air surrounding it. This energy causes the air molecules to vibrate as the sound wave moves out and away from the source (Note: for our purposes we can assume the medium is air). The vibrating air molecules will have pressure variations that fluctuate above and below atmospheric air pressure. (See illustration on Slide 5)

When the sound wave reaches a human, it causes the ear drum to vibrate. It is the movement of the ear drum that allows humans to perceive (hear) the pressure changes around the ambient air pressure. Thus, SOUND is detected.(So by definition - if a tree falls in the middle of the woods and nobody is there to hear it (no animals, humans, or artificial ear such as a microphone), it DOES NOT MAKE A SOUND!! It does, however, create a sound wave or pressure disturbance, which will dissipate over distance.)



3

DEFINITION OF NOISE

Noise is defined simply as unwanted sound.

People often ask what is the difference between NOISE and SOUND. Physically, there are one in the same. However, what may be sound to one person may also be noise to another. So when you see the words noise and sound used interchangeably, by physical definition they are the same thing.



4

SOUND PROPAGATION

The sound wave is transmitted through the medium by means of a chain reaction.

As mentioned previously, when a disturbance occurs it puts energy into the air surrounding it. This energy causes the air molecules to vibrate as the sound wave moves out and away from the source. As the air molecules vibrate they actually collide with their neighboring molecules, transferring their energy, which in turn is transferred to the next molecule, and so on and so on, etc. This process continues until the energy dissipates, or decays to the point that no more energy exists. So as you can imagine, this chain reaction is how the sound wave is transmitted away from a noise source. The more energy put out by the source, the louder the noise will be and the further it will carry into the distance.



5

FREQUENCY

The Frequency of a sound is the number of times per second that a disturbance passes through both its positive and negative excursions around atmospheric pressure. The number of cycles per second is termed Hertz (Hz).

Air has both mass and elasticity, which allow the sound wave to propagate. As a molecule is vibrates, it compresses a layer of air surrounding it. This compression creates a positive pressure above the atmospheric pressure. The elasticity of the air is the characteristic that will pull the molecule back to its original position, thus creating what is called a rarefaction, or negative pressure below atmospheric pressure. See the figure for an illustration of this effect.

The number of times per second (also called cycles) the sound wave passes through a positive (compression) and negative (rarefaction) excursion around atmospheric pressure is called its Frequency.

Next, the term Hertz, abbreviated Hz, is used to describe the frequency or cycles per second. For example, 500 cycles per second may also be referred to as 500 Hz.



6

PERIOD

Period = the time it takes to complete one cycle.

It is related to the frequency by:

T=1/f seconds

The term Period is symbolized by T. So if you use 500 Hz, the Period or time to complete one cycle would be:

T = 1/500 = 0.002 seconds



7

AMPLITUDE

The distance a particle moves from atmospheric pressure is called its Amplitude.

It determines how loud a sound will be.

The magnitude or how far a particle (molecule) is moved above or below atmospheric pressure is called its Amplitude (See figure). This determines how loud the sound or noise will be.



8

WAVELENGTH

The distance between like points on two successive waves is called the Wavelength, and symbolized by (Greek symbol Lambda).It is related to the frequency (f) and speed of propagation (c) by:

Wavelength () = c/f = cT (feet)

Each frequency will have a different wavelength. In the equation above, the term c is the speed of sound in air, which is equal to 1128 ft/s, or 344 meters/second, at standard temperature and pressure. So the wavelength of 500 Hz would be determined by going:

= 1128 ft/s / 500 cycles/sec = 2.2 ft/cycle, or simply 2.2 feet

Note we are interested in the wavelength per one cycle, so we can drop the cycle unit and simply refer to in terms of feet or meters.



9

WAVELENGTH OF SOUND IN AIRfrequency wavelength31.5 Hz 35.8 ft. (11.6 m)

63 17.9 ft (5.8 m)

125 9.0 ft. (2.9 m)

250 4.5 ft (1.5 m)

500 2.2 ft. (0.7 m)

1000 1.1 ft. (.35 m)

2000 6.7 in. (17 cm)

4000 3.4 in. (8.6 cm)

8000 1.7 in. (4.3 cm)

This table presents the wavelength for sound in air at each octave-band frequency. The key point to observe is that low frequencies and long wavelengths and high frequencies have very short wavelengths. Toward acoustical materials used to absorb and block (isolate) sound transmission, it is much easier to treat the shorter wavelengths (absorb and isolate) than the long wavelengths in the low frequencies.

Similarly, environmental or community noise problems typically involve the low frequency sounds, because these wavelengths can travel much farther than high frequency wavelengths.



10

SPEED OF SOUND

The speed at which sound travels depends on the density and elasticity of the medium.

In the case of fluids and gases, temperature must also be considered.

As mentioned at the start, the medium we are most concerned with is air. However, there will be times when we may need to consider the wavelengths for other mediums, such as liquids, gases, or solids.



11

SPEED OF SOUNDft/sec m/sec

Air 1100 360

Lead 4000 1300

Water 4500 1460

Concrete 10,000 3250

Glass 12,000 3900

Wood 14,000 4500

Steel 17,000 5520

Iron 17,000 5520

This table presents the speed of sound for a variety of common mediums. Note how air is a relatively poor transmitter of sound waves when compared to these other mediums. As you can see in the table, the wavelength on steel is approximately 17 times greater than that of air. This is why sounds can travel great distances in steel (for example, steel pipe lines) without losing its energy as fast as that in air.



12

SOUND PRESSURE

The oscillation of the sound wave around atmospheric pressure.

The vibration of air molecules or particles around atmospheric pressure is called the sound pressure. Keep in mind sound pressure is the EFFECT of a disturbance in air.



13

SOUND POWER

Sound power is the energy that causes the air particles to vibrate.

The actual CAUSE of a disturbance, and the resulting vibration or chain reaction effect, is the power, called sound power.

It is important to remember Sound Power is the Cause of a disturbance and Sound Pressure is the Effect.

The application of sound power and sound pressure is presented later in this section, which should clear up any confusion that may exist regarding the differences between these two entities.



14

SOUND MEASUREMENT

The range of sound powers and sound pressures is very wide. In order to cover this wide range while maintaining accuracy, the logarithmic decibel (dB) scale was selected.

The intensity of the faintest sound that the normal person can hear is about 0.0000000000001 watts/m2, while the intensity of the sound produced by a Saturn rocket at liftoff is greater than 100,000,000 watts/ m2. This is a range of 100,000,000,000,000,000,000. Given this extremely large range in values, there needed to be a better way to express or represent these numbers. By using logarithms of these numbers, as compared to a reference value, we can form a new measurement scale in which an increase of 1.0 represents a tenfold increase in the ratio (also called a 1.0 bel increase). The application of logarithms is evolved to the use of 10 subdivisions of a log value, which is the term you may be familiar: decibels

Decibels is abbreviated to the term dB. The lower case d represents deci, or 1/10th of a bel. The capital B stands for bel, named after Alexander Graham Bell, inventor of the telephone. Dont ask why there is only one l in bel.



15

DECIBEL - A dimensionless unit related to the logarithm of the ratio of a measured quantity to a reference quantity.

As you will see in the next few slides, the dB is a dimensionless quantity, which is related to an internationally agreed upon reference value.



16

SOUND POWER LEVEL - The acoustical power radiated by a source with respect to the standard reference of 10-12 watts.

Lw = 10 Log (W/Wre)

The international reference for power is 10-12 watts. Now because we are converting a sound power into a Level, or dB, the formula is as shown above. The term Lw is used to represent the Sound Power Level. The w subscript identifies the fact this equation deals with power in units of watts.

To demonstrate how this equation works lets look at an example:Determine the sound power level of a small electric motor that generates 0.1 watts of sound power:

Lw = 10 Log (W/Wre)Lw = 10 Log ( 0.1/10-12 )Lw = 110 dB

The key point here is that even a small amount of sound power (0.1 watts) can produce a rather large sound power level.



17

SOUND PRESSURE LEVEL - The sound pressure measured at a certain distance from a source with respect to the standard reference of 20 x 10-6 Pa.

Lp= 10 Log (P/Pre)2

Which equals:

Lp= 20 Log (P/Pre)

To convert the sound pressure into a decibel value, again logarithms are used. As with sound power, the sound pressure also has its own internationally accepted reference value, which is 20 X 10-6 Pascals (Pa). Now sound power varies proportionally to the square of sound pressure: (watts) (pressure)2Therefore, through application of log algebra, the squared value can be carried to the front of the equation, which results in 20 log (20 comes from 2 X 10).

Remember - Lp is the effect of a disturbance or the sound we hear, and Lw is the cause (power) of the disturbance that puts the air molecules into motion. The microphone on all sound level meters can only measure Lp and there is no direct way to measure Lw.



18

Note the large range in sound pressure levels. To make these numbers more usable, they were converted to decibels using log ratios to a standard reference value.



19

The relationship between sound pressure level and sound power level is expressed as :

Lp= Lw + K

Lw = Sound Power Level (cause)

Lp = Sound Pressure Level (effect)

K = constant, depending on environment

Lp and Lw are related by the equation shown above. The K factor is a constant based upon the acoustics of the environment. The best way to explain the differences is to consider an analogy:Say we put a 100 watt light bulb in the center of a small room that is completed painted with flat black paint. The illumination in the room will seem rather dim or dull when compared to the identical set-up in a second room that is pointed with glossy white paint. As you can imagine the white room will be significantly brighter.

The same thing happens with sound. If you have a machine with a Lw = 90 dB and place it in a small room with a concrete floor, ceiling and brick walls, the sound pressure level, Lp (that we hear) could be as much as 110 dB due to the reflectionand build-up of sound inside the room. Conversely, if we take the same machine and place it on a pad outside, the Lp may only be on the order of 92 dB. Note the sound power is identical in both scenarios, but the result or effect is dramatically different. This is due to the environment (K factor) that combines with the sound power level to produce a specific sound pressure level. Note - The Room Acoustics section will expand on all the variables that comprise this K factor.



20

There are three ways to add decibels together:

Equation Method

Table Method

Spreadsheet Method

In many practical situations it is necessary to determine the combined effect of several noise sources. However, since sound levels are logarithmic quantities, they cannot be combined by simply adding or subtracting the individual levels.



21

EQUATION METHOD (Most accurate)

Lp (total) = 10 Log (10Lp1/10 + 10Lp2/10 + )

Where,

Lp1 = Sound Level of 1st source,

Lp2 = Sound Level of 2nd source,

etc.

The actual acoustic intensities represented by the logarithmic expressions must be determined by taking antilogs of the level readings. The intensities can be added together and the new level is determined from the logarithm.

In the equation method, the anti-log of each sound level is first calculated. To get the anti-log: the value of 10 is raised to the power of each individual sound level divided by 10, then all resultant values are arithmetically added together. Their logarithm is calculated, and multiplied by 10 to obtain the total sound pressure level (Lp).



22

EXERCISE:

Add 85 dB + 87 dB + 90 dB + 71 dB using the equation method.

Use the equation:

Lp (total) = 10 Log (10Lp1/10 + 10Lp2/10 + )

and a pocket calculator (need a log function on the calculator).

In the equation:

Lp (total) = 10 Log (10Lp1/10 + 10Lp2/10 + )the value for Lp1 is 85, for Lp2 is 87, for Lp3 is 90 and Lp4 is 71, so: (use your calculator to practice using the equation method)

Lp (total) = 10 Log (1085/10 + 1087/10 + 1090/10 + 1071/10 ), dB

Lp (total) = 10 Log (108.5 + 108.7 + 109.0 + 107.1 ), dB

Lp (total) = 10 log (1,830,004,254), dB

Lp (total) = 10 (9.262) = 92.6 dB Note - rounded to nearest 10th.



23

TABLE METHOD (Less accurate, but easier)

Example: Add 90 dB + 95 dB + 88 dB

95

90

88

Recommended Steps:Step 1 - list all sound levels in a column from the highest value to lowest (as shown in the slide above). Step 2 - start at the top of the column and take the first two values, which are 95 and 90 dB. Subtract 90 from 95 to get a numerical difference of 5.Step 3 - use the table to determine the amount that needs to be added to the higher value. For example, with a difference between the two sound levels of 5 - you would add 1.2 to the higher value (95): so 95 + 1.2 = 96.2 dBStep 4 - now take 96.2 and the next value in the column, which is 88, and determine the numerical difference: 96.2 - 88 = 8.2Step 5 - again go to the table and look up how much to add to the higher value with a difference of 8.2: add 0.6 so 96.2 + 0.6 = 96.8 dB

The resultant sound level from all three values (noise sources) will be 96.8 dB.So keep in mind, when you add more equipment to a room, the sound level from the new equipment will add to the existing ambient or background level of the room.



24

The Spreadsheet Method:

Add 85 dB + 87 dB + 90 dB + 71 dB using the Spreadsheet Method.

Note: Use the Calculation Aid Decibel Addition Excel spreadsheet



25

dB ADDITION AND SUBTRACTION

This program adds or subtracts dB levels.

Enter dB levels to be added:(antilog Lp/10)

1 85 3.16E+082 87 5.01E+083 71 1.26E+074 5 6 7 8 9

10 11 12

89.19 dB

Enter dB levels to be subtracted:(antilog Lp/10)

93 2.00E+09 minus 90 1.00E+09

89.98 dB

Note this spreadsheet will be provided to you during the course.



26

HUMAN HEARINGThe human ear responds to a wider range of frequencies (20 -20,000 Hz). It is most sensitive around 3000 Hz, and least sensitive in the lower frequencies.

The ability of humans to hear sound is bounded by 20 - 20,000 Hz. In other words, if a sound is at 21,000 Hz, it will not be heard by the human ear. Similarly, if a sound is at 15 Hz, it will not be heard by a human listener.



27

WEIGHTING CURVES

Sound Pressure Level becomes SOUND LEVEL when a weighting has been applied. The weighting networks are useful to compare sound levels to how the human ear hears and is effected by continuous exposure.

When a weighting network is applied to a sound pressure level, we no longer have a pure pressure relationship, but instead have a relative level to human listeners. So when you see the term sound level it implies the true sound pressure level has been corrected to specific weighting network. The primary weighting network for industrial noise is the A-weighted network.



28

WEIGHTING CURVES (contd)

The A-weighted sound level provides a single number rating that correlates reasonably well with human hearing-damage risk due to exposure to continuous sound.

Humans are more sensitive to middle frequency sounds (500 - 4,000 Hz) than they are to low or very high frequency sounds. The A-weighted chart shown here lists the correction values to be subtracted from, and in a few instances added to, the pure or true sound pressure level for each octave-band. For example, in the chart a pure-tone sound pressure level of 100 dB at 250 Hz will actually be heard by a human listener as 83.9 dBA at 250 Hz (100 - 16.1 = 83.9 dBA). It is critical to note that when the specific A-weighted correction value is subtracted from the sound pressure level, in dB, the result is then expressed in units of dBA. So the A that follows the dB means it is an A-weighted value.

Because A-weighted sound levels correlate well with human hearing and its hazardous effects, this is why all noise regulations use the A-weighted values or dBA.



29

FREQUENCY ANALYSIS

Most industrial noise is made up of a very large number of individual frequency components.

It is important to characterize noise in terms of its frequency content in order to control it.

Toward noise control measurements, it is important to use a sound level meter that has an Octave-band filter. This instrument set-up will allow the surveyor to not only measure the overall dBA values, but also the individual octave-band frequency data.



30

Filters in a sound level meter are used to bread down the noise into smaller frequency ranges.

The OCTAVE BAND and THIRD-OCTAVE BAND filters are most commonly used.

The data obtained with an octave-band or 1/3 octave-band filter is useful toward (1) identifying the origin of the noise source, and (2) selection of the appropriate noise control products and materials. These two items will be explained in detail in the Principles of Noise Control and Room Acoustics sections of this training material.

The chart shown here presents the frequency ranges for both octave-band and 1/3 octave-bands. Note: the center band frequency (fc) is the actual name used to describe a frequency range. For example, an fc at 500 Hz will take into account all sound pressure levels occurring from 355 - 710 Hz, using the octave-band ranges. In other words, if a pure-tone is occurring at 660 Hz, it will appear on the sound level meter in the 500 Hz octave-band setting or mode of the instrument. (Note: some textbooks refer to octave-bands as 1/1 octave-bands - just remember they are the same thing.)

1/3 octave-bands are used whenever the surveyor desires more detailed information. In reality 1/3 octave-band measurements simply divide the full octave-band data into thirds (three data points). So if you would logarithmically add all three 1/3 octave-band readings together - it must equal the value measured with the full octave-band setting.

Documents

Fundamentals of Sound