3.2 INTENSITY LEVEL METERS

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There are some situations where we would like to measure the intensity

directly, instead of measuring the sound pressure level and attempting to

calculate the intensity from this measurement. In addition, the location of a

specific noise source may be determined from the directivity pattern associated

with intensity level measurements. The intensity level meter is a helpful

tool for location of sources of noise problems in a machine, such as noise

produced by bearing failure, internal impact problems, etc. A typical sound

intensity meter is shown in Fig. 3-5.

The acoustic intensity is the time-averaged value of the product of the

acoustic pressure and acoustic particle velocity.

I ј_p_u

In the intensity probe, two microphones are placed face-to-face at a known

spacing _x, as shown in Fig. 3-6. Typically, the spacing is 6mm for frequencies

between 250 Hz and 12 kHz, 12mm for the 125 Hz to 5 kHz range,

and 59mm for frequencies between 31.5 Hz and 1.25 kHz (Beranek and Veґ r,

46 Chapter 3

FIGURE 3-5 Sound intensity meter. The two opposed microphones may be

observed in the upper part of the figure. (By permission of BruЁ el and Kjaer.)

Copyright © 2003 Marcel Dekker, Inc.

1992). As we will show in Chapter 4, the particle velocity and the acoustic

pressure are related by:

_ u ј _

1

_

р

@p

@x

dt _ _

1

_

р

р pB _ pAЮ

_x

dt (3-1)

where pA and pB are the sound pressures indicated by microphone A and B,

respectively. The integration of the acoustic pressure is carried out in an

analyzer in the intensity measuring instrument. The average acoustic pressure

is:

_ p ј 1

2 р pA ю pBЮ

The time-averaging of the acoustic particle velocity and average acoustic

pressure may be done directly by using integrators and filters.

The accuracy of the intensity level meter in direct measurement of the

intensity is a function of the wavelength of the sound and the spacing of the

two microphones. Suppose the instantaneous acoustic pressure at a specific

time is given by:

pрxЮ ј pm sinрkxЮ (3-2)

where pm is the peak amplitude, k is the wave number, and the coordinate x

is measured from the center of the spacer. The exact expression for the

derivative in Eq. (3-1) is:

@p

@x ј pmk cosрkxЮ ј pmk рat x ј 0Ю (3-3)

The approximation in Eq. (3-1) is:

pB _ pA

_x ј

pmЅsinр1

2 k_xЮ _ sinр_ 1

2 k_xЮ_

_x ј

2pm sinр1

2 k_xЮ

_x

(3-4)

The pressure pB is measured at the position x ј ю1

2_x, and the pressure pA

is measured at x ј _1

2_x.

Acoustic Measurements 47

FIGURE 3-6 Sound intensity probe schematic.

Copyright © 2003 Marcel Dekker, Inc.

The error in the intensity measurement is proportional to the error in

the derivative approximation:

error ј

pmk _ Ѕ2pm sinр1

2 k_xЮ=_x_

pmk ј 1 _

2 sinр1

2 k_xЮ

k_x

(3-5)

As the dimensionless parameter k_x approaches zero, the second term in

Eq. (3-5) approaches 1, and the error approaches zero.

The intensity probe is highly directional, so care must be taken to

orient the probe such that the sound waves are incident along the probe

axis. If the incident sound wave makes an angle _ with the probe axis, the

indicated intensity I will deviate from the intensity along the axis Io according

to the following expression (Beranek and Veґ r, 1992):

I ј Io cos _

One of the advantages of the use of the intensity meter is that steady

background noise does not affect the meter indication. The integration

procedure eliminates steady background noise components, so accuracy

on the order of 1 dB may be achieved when the background noise level is

as much as 10 dB higher than the noise to be measured. Another advantage

of the intensity meter is that its directional characteristics may be used to

identify the direction of significant noise sources relative to the instrument.

For example, the intensity level meter is well suited for acoustic troubleshooting

tasks to locate the specific problem causing excessive noise in a

machine. A disadvantage of the intensity meter is that it is usually more

expensive than a basic sound level meter.

Example 3-1. Determine the error in the intensity meter reading if the

microphone spacing is 6mm (0.236 in). The frequency of the sound wave

is 12 kHz, and the speed of sound in the air around the microphone is 346 m/

s (1135 fps).

The wave number is:

k ј

2_f

c ј р2_Юр12; 000Ю

р346Ю ј 217:9m_1

Then,

1

2 k_x ј р1

2Юр217:9Юр0:006Ю ј 0:6537

The percentage error is found from Eq. (3-5).

error ј 1 _

sinр0:6537Ю

р0:6537Ю ј 1 _ 0:9303 ј 0:070 or 7% error

48 Chapter 3

Copyright © 2003 Marcel Dekker, Inc.

If we wish to limit the error to 5%or less for the conditions in this example,

the microphone spacing would need to be reduced to about 5.1mm(0.20 in).

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