Information on Sound Power and Sound Pressure
FLUID POWER  Design Data Sheet 24
The Nature of Sound
Airborne sound (including noise) is a variation in PSI air
pressure in the audible range, and sound pressure can be measured
by its force against the diaphragm of a microphone. Sound waves,
unlike light waves, are longitudinal vibrations of air molecules
moving back and forth in the direction of the traveling wave.
Energy from a sound generator sets sound waves in motion, and they
travel approximately 1,100 feet per second in air.
As sound waves radiate outward from their source, their
intensity diminishes as the square of the distance traveled,
starting with a first measuring point at least 2 or 3 times the
largest dimension of the noise source. On small components such as
pumps, this first measuring point is taken as 3 feet or 1 meter
from the center of the pump.
The wide range of sound intensity and sound pressure in the
audible range complicates the problem of rating noise strength. The
human ear can hear, without damage and without discomfort, sound
pressures 10,000 times greater than the weakest sound it can
detect.
Because of this extremely wide range, noise measuring
instruments are usually calibrated in decibels (dB) instead of in
PSI. The dB scale is logarithmic, which compresses the upper end of
the scale and allows ratings to be given in not more than 3 digits
(120 dB, etc).
An important fact to remember about decibels is that they are
merely ratios, and only become absolute values of power or pressure
when referred to a fixed base. In acoustics, the sound pressure
which is barely audible is 3 × 10 PSI, and this has been assigned a
value of 0 dB. It takes a calculated value of 10.042 dB of acoustic
power (from a pump, for example) to produce a pressure level of 0
dB at a distance of 3 feet from the pump. The reference, or base,
level for acoustic power is taken as 1 × 10^{12}
watts.
A person can comfortably tolerate sound pressure levels up to 80
dB. Between 80 and 90 dB he might show some intolerance to the
noise, but above 90 dB the average person can tolerate it only for
short periods.
Threshold of sound 
0 dB 

Noisy factory 
90 dB 
Average hearing threshold (whisper) 
16 dB 
Heavy city traffic 
100 dB 
Very quiet office 
40 dB 
Rock band 
120 dB 
Residential kitchen 
55 dB 
Pain threshold 
140 dB 
Normal conversation 
60 dB 
Bad weather siren 
140 dB 
Very noisy office 
70 dB 
Structural Ear Damage 
140 dB 
Loud radio 
7 dB8 
Jet Engine 
160 dB 
WalshHealey limit for 8hour
exposure (85 dB future) 
90 dB 
Definition of the Decibel
On the decibel scale used for expressing the total amount of
acoustic power radiated from a noise source, the dB level is
defined as 10 times the logarithm (to the base 10) of the ratio
between the sound level and 0 dB (1 × 10^{12} watts).
However, since sound pressure at any radius from the source is
proportional to the square root of the sound power producing it,
the decibel scale for expressing the sound pressure is defined as
20 times the logarithm of the ratio between the measured sound
pressure and 0 dB, because to square a number its logarithm must be
doubled. The accepted reference level for 0 dB on the pressure
scale is 3 × 10^{9} PSI. (0.0002 microbar).
Acoustic Power Radiation
Figure 1.
Doubling the sound power at its source
increases its level by 3 dB, and increases the sound
pressure level at all distances by the same 3 dB.
If acoustic power at the source is increased, the chart below
gives examples of how to calculate the increase on the dB power
scale. The first example shows that if the sound power is doubled,
the radiated dB level increases by approximately 3 dB.
If one pump is rated at 85 dB and another identical pump is
added, the sound power increases to 88 dB. If a third pump is
added, the power level becomes 89.77 dB, etc.
Increasing the sound power, for example by 5 dB, also increases
the sound pressure by 5 dB at all distances.
Power
Increase 
Examples of
Calculations of Sound
Power dB Increase at the Source 
2 Times 
Increase = 10 × log 2 = 10 × 0.301 = 3.01 dB. 
3 Times 
Increase = 10 × log 2 = 10 × 0.301 = 3.01 dB. 
4 Times 
Increase = 10 × log 2 = 10 × 0.301 = 3.01 dB. 
1,000 Times 
Increase = 10 × log 2 = 10 × 0.301 = 3.01 dB. 
Sound power at the source cannot be measured; it can be
calculated by making a dB pressure measurement at any distance,
then using the formula: dB (power) = dB (pressure reading) + 20 ×
logarithm of distance in feet + 0.5 dB. At 3 feet: dB (power) = dB
(pressure) + (20 × 0.477) + 0.5 dB.
"A" Weighted Sound Pressure Levels
Figure 2. Whether a sound is objectionably loud
depends on its frequency as well as on its intensity. Higher
frequency sounds are less tolerable and do more damage to the ear
than do sounds of the same intensity at lower frequencies.
Figure 2. "Noise"
intolerance depends on frequency
as well as on intensity of the sound source.
The permissible noise exposure levels stated in the WalshHealey
Act are in the "A" weighted frequency response network, and marked
"dBA".
Noise level meters have a selector switch for setting their
sensitivity over the audible range either to the "A", "B", or "C"
weighted response characteristics. When set on the "A" scale,
filters in the electronic circuit of the meter give it about the
same response as the human ear over the audible range, and meter
readings are specified in "dBA''. This scale is always used when
measuring sound pressure imposed on an operator because it
totalizes the full range of frequencies which cause discomfort and
ear damage. The "B" and "C" weighted scales on the meter also have
filters which give the frequency response curves shown on the
graph. They are used mainly for scientific measurements when
tracing the source of noise.
Noise Level at the Operator's Position
Figure 3. The objective, of course, in making
noise measurements is to be sure the sound pressure level on the
operator's ears does not exceed an acceptable level. A hydraulic
pump rated at 120 dB may or may not be too noisy, depending on its
distance from the operator.
The chart under Figure 3 gives examples of how
to calculate decrease in dB pressure level as the sound source is
moved further from the operator, based on a reference position
located 3 feet from the source. The first example shows that if the
separation distance is doubled (as referred back to the 3foot
reference point), the sound pressure level is reduced by
approximately 6 dB from its original level, etc.
Figure 3. Sound
pressure on the listener's ears
decreases as the square of the distance from the source.
Increased
Distance 
Examples of Calculations for dB Sound Pressure
Decrease in Free Atmosphere Conditions 
2 Times 
Decrease = 20 × log 2 = 20 × 0.301 =
6.02 dB. 
3 Times 
Decrease = 20 × log 3 = 20 × 0.477 =
9.54 dB. 
4 Times 
Decrease = 20 × log 4 = 20 × 0.602 =
12.04 dB. 
25 Times 
Decrease = 20 × log 25 = 20 × 1.40 =
28.0 dB. 
If the dB power rating of a pump is known, the dB pressure level
at any distance can be calculated with this formula: dB (pressure)
= dB (power)  20 log distance in feet  0.5 dB.
Acoustics Measurements Summary
Sound is measured with an instrument which includes a microphone,
an electronic amplifier with filters, and a voltmeter having a
scale graduated logarithmically and marked in decibels (dB).
However, a sound meter cannot measure the acoustic power being
radiated from a sound source. Instruments can only measure the air
pressure produced at varying distances from the source by the
energy of the sound waves. From pressure measurements, the acoustic
power at the source can be determined mathematically.
If it were possible to have 5 identical pumps set up so they
were always equidistant from a sound meter, and if the meter
reading with one pump running was 70 dB at a distance of 3 feet
from the meter, these meter readings might be expected at other
distances and other running conditions:
No.
of Pumps
Running 
Distance from Center of Pumps 
3
Feet 
6
Feet 
12
Feet 
24 Feet 
1 Pump 
70 dB 
64 dB 
58 dB 
52 dB 
2 Pumps 
73 dB 
67 dB 
61 dB 
55 dB 
3 Pumps 
74.8 dB 
68.8 dB 
62.8 dB 
56.8 dB 
4 Pumps 
76 dB 
70 dB 
64 dB 
58 dB 
5 Pumps 
77 dB 
71 dB 
65 dB 
59 dB 
Note from this chart that dB power levels Increase by 3 dB each
time the radiated sound power doubles, but the sound pressure read
on a meter decreases by 6 dB each time the distance from the 3foot
reference position doubles. Sound pressure decreases faster with
distance than it does by decreased sound power because sound
pressure is considered to be proportional to the square root of the
radiated sound power.
In a later issue we will summarize points on the original system
design to obtain a quieter hydraulic system.
Download a PDF of Fluid
Power Design Data Sheet 24  Information on Sound
Power and Sound Pressure.
© 1990 by Womack Machine Supply Co. This
company assumes no liability for errors in data nor in safe and/or
satisfactory operation of equipment designed from this
information.
