40.2 Mirror–Microphone System

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40.2.1 Principle of Measurement

A mirror– microphone system consists of a reflector

of elliptic or parabolic shape and an omnidirective

microphone located at its focus [6,7].

Figure 40.4 shows the layout of a reflector of elliptic

shape, an omnidirective microphone, and a noise

source. Here, S and S0 denote the front and back

surfaces of the mirror, respectively; PðrÞ denotes the

pressure field on this configuration; PiðrÞ denotes

the pressure field of free space; rm is the position of

the microphone; r is a point on the mirror surface.

The normal, n0; directs toward the medium.

Using Green’s theorem, the pressure at the

microphone position PðrmÞ is obtained by

PðrmÞ ¼ PiðrmÞ þ

ð ð

ðsþs 0Þ

PðrÞ

›

›n0

􀀐

eikRm

4pRm

" #

d2r ð40:8Þ

where k ¼ 2pf =c0 is the wave number, f is the

frequency of sound, c0 is the speed of sound, and

Rm ¼ lr 2 rml is the distance between the microphone

and the mirror surface. If the wavelength is

sufficiently smaller than the diameter of the

reflector, the pressure field PðrÞ is approximated

by 2PiðrÞ on the front surface, S; and by zero on the

back surface, S0: In such a frequency range, the

incident field term PiðrmÞ can be ignored. With

these approximations, assuming that the noise

source is a monopole type point source located at a

position, rs; Equation 40.8 reduces to

PðrmÞ ¼ 2

mð f Þ

8p 2

ð ð

s

eikðRm þRs Þ

RmRs

ik 2

1

Rm

􀀏 􀀐

􀀐 cos uðrÞd2r ð40:9Þ

Here, mð f Þ is the amplitude of the mass-flux rate of the source, Rs ¼ lr 2 rsl is the distance between the

sound source and the mirror surface and the angle uðrÞ is defined in Figure 40.4. When the noise source is

located at the far focus of the mirror, the sound pass length Rm þ Rs is constant with respect to r; and a

strong signal is obtained. As the noise source is moved away in the direction perpendicular to the mirror

axis, the variance of the sound pass length, Rm þ Rs; due to the position r increases, and thus the

microphone signal drops off due to interference (see Figure 40.5, which we call the “directivity pattern”).

The ratio of the peak level to the free field level at the microphone, G; is referred to as the “gain factor.”

The spatial resolution of the mirror is characterized by the displacement of the mirror position, w; at

which the microphone signal drops off by a given relative amount, such as 3 dB. The quantities G and w

w

3dB

0

G

SPL at microphone position

(re.SPL in freefild)

Displacement of

the mirror

FIGURE 40.5 Directivity pattern of a mirror– microphone

system.

Microphone

= Near focus

Rs Rm Far focus

r m

n0

θ

Noise source

D

B

L

Reflector

r

rs

S′

S

FIGURE 40.4 Layout of a reflector, microphone, and

noise source.

40-4 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

can be related to the mirror geometries in Figure 40.4 by

G < 10 logðCD4=l2B2Þ ðC ¼ const:Þ ð40:10Þ

w / lL=D ð40:11Þ

The gain factor, G; increases with frequency at the rate of 6 dB per octave, and the spatial resolution, w; is

inversely proportional to the frequency. The lower frequency limit is decided by the size of the mirror. On

the other hand, there is no higher frequency limit, except for the capacity of an omnidirectional

microphone itself. Thus, measurements with the mirror– microphone system are more suited to a scaled

model test.

40.2.2 Applications

The mirror– microphone system has proved useful for identification of a noise source because of its

directional property [8 – 10]. A scan of the source region produces a noise source map. It has an

advantage in that the measurement is possible at a far field and it needs only one sensor, but has a

disadvantage in that the measuring process is a time-consuming task.

Figure 40.6 shows an example of source maps of aerodynamic noise generated by a one-fifth scale

high-speed train model, obtained from measurements by a mirror– microphone system, in a wind tunnel

test. The surface of the car model is divided into several noise-source areas and the noise-source

distribution in each area is measured by traversing the mirror– microphone system over the surface. The

diameter and focal distance of the reflector are 1.7 and 3 m, respectively. Detailed maps of noise-source

strength are obtained, which show that aerodynamic noise from high-speed trains is generated in

relatively localized areas, namely, the local surface structures. The mirror– microphone system can be

used for the measurement of the source distribution of a moving noise source. Figure 40.7 gives a time

FIGURE 40.6 Noise-source distribution of a one-fifth scale Shinkansen car model in a wind tunnel test measured

with an elliptic mirror– microphone system.

Instrumentation 40-5

© 2005 by Taylor & Francis Group, LLC

history of noise from a high-speed train measured with a parabolic mirror– microphone system, the

diameter of which is 1 m. Peaks of the time history correspond to pantographs, doors, gaps between cars

and the step-up of windows, which shows that they are main noise sources.

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