Sound Pressure, Power, and Intensity

Chapter 6

Sound Pressure/Power/Intensity All three terms describe physical

sensations. All three are perceived on a linear

scale when sensation is multiplied. Psychophysics

Decibels Decibel scales compare two

quantities. Dimensionless unit. Abbreviated dB

Sound Power Level

Defines the decibel difference between two sound power levels.

Usually the comparison is between a power level and a fixed reference (W0 = 10–12 W)

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ΔL = L2 − L1 =10logW2 /W1

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LW =10logW /W0

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LW =10logW

W0

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Important Power Relationships log 2 = 0.3 so 10 log 2 = 3 dB

Doubling the power equals a 3 dB gain log 1/2 = 0 – 0.3 so 10 log 1/2 = –3 dB

Halving the power equals a –3 dB reduction –3 dB represents the half-power point

Power is proportional to A2 (0.7072 = 0.5)

More Fun with Logarithms If 10 log 2 = 3, then 10 log 4 = 6. 10 log 10 = 10 10 log 5 = 7 (5 = 10/2)

Intensity Level and Pressure Level Sound Power Level refers to the

power at the output source. It is not meaningful to speak of the

sound power level at some point in the room.

At any given point you can measure the Sound Intensity Level and/or Sound Pressure Level

Equation for Intensity Level

is the reference intensity level. Sound Intensity Level in decibels:

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I0 =10−12 W/m2

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LI =10log I /I0

Equation for Pressure Level

is the reference pressure level, the threshold of audibility.

Sound Pressure Level in decibels:€

p0 = 2 ×10−5 N/m2

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Lp = 20log p / p0

Intensity/Pressure Relationship Intensity is related to pressure

squared. At ordinary temperatures and air

pressure, Sound Intensity Level and Sound Pressure Level are almost equal. We can assume that they are equal.

Inverse log To get from decibels (SPL, SIL,

PWL) requires an inverse log operation Calculator note: In x; INV then log; 10

x

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W =W0 INV logLw (dB)

10

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I = I0 INVlogLI10

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p = p0 INVlogLp20

Relation of Intensity to Power Sound Power Level refers to power

at the output source Power radiates out from a center,

becoming Intensity. (flow of energy across a unit area)

Intensity at Source Power radiating from a surface

area. Intensity and Sound Intensity Level

Free Field In a Free Field, sound radiates equally in

all directions. Intensity varies as 1/r 2 (pressure 1/r ). Power distributed over the surface of an

expanding sphere with area 4πr2. I = W/ 4πr2

Sound Intensity Level drops 11 dB the first meter, and 6 dB every time the distance is doubled.

Hemispherical Field Sound is rarely radiated equally in all

directions. Usually, the sound source is on a hard,

reflective surface. Power is distributed over a hemispherical

field, with a surface of 2πr2. Sound Intensity Level drops 8 dB for first

meter, and 6 dB for each doubling of distance.

Remember, SPL roughly equals SIL.

PWL to SIL and SPL A change in PWL will result in the

same change in either SIL or SPL.

Multiple Sources Two sources combining (with same dB)

Power standpoint: doubled, therefore +3dB

Leads to a +3dB change in SPL at any given point.

Pressure and Intensity Intensity proportional to p 2 Add intensities (observed intensity) Add square of each pressure, divided by

square of reference pressure

Loudness Level Sensitivity of the ear varies with

frequency and quality of sound. Fletcher-Munson Curves (Equal

Loudness) p. 107. (phons ) Relative insensitivity to low frequency

sounds leads to weighting networks in sound-measuring devices. C: mostly flat A: low-frequency rolloff in gain

(compensates for insensitivity of ear)