Handbook for Sound Engineers

Microphones 535

times of waves b and c compared to wave a. Note that

they increase with the angle of sound incidence.

The resulting pressure at the capsule can be calcu-

lated by the sum of all particular waves generated over

the tube’s length, all with equal amplitudes but different

phase shifts. The frequency and phase response curves

can be described by

(16-27)

where,

P(T) is the microphone output at a given angle of sound

incidence,

P(T = 0°) is the microphone output along principal axis,

O is the wavelength,

L is the length of the tube,

T is the angle of sound incidence.

The calculated curves and polar patterns are plotted
in Figs. 16-95 and 16-96 for a tube length of 9.8 inches
(25 cm) without regard to the low-frequency directivity
caused by the rear inlet. The shape of the response
curves looks similar to that of a comb filter with equidis-
tant minima and maxima decreasing with 6 dB/octave.
The phase response is frequency independent only for
frontal sound incidence. For other incidence angles, the
phase depends linearly on frequency, so that the resulting
pressure at the capsule shows an increasing delay time
with an increasing incidence angle.
In practice, interference tube microphones show
deviations from this simplified theoretical model.
Fig. 16-97 is the polar pattern of the Sennheiser
MKH 60P48. The built-in tube delivers a high-
frequency roll-off for lateral sound incidence with a
sufficient attenuation especially for the first side lobes.
The shape of the lateral inlets as well as the covering
material influences the frequency and phase response
curves. The transition frequency can be lowered with an
acoustic mass in the frontal inlet of the tube to increase
the delay times for low frequencies.
Another interference tube microphone is the Shure
SM89, Fig. 16-98.^9 In this microphone, a tapered
acoustic resistance is placed over the elongated interfer-
ence tube slit, varying the effective length of the tube
with frequency so that L/M (the ratio of tube length to
wavelength) remains nearly constant over the desirable
frequency range. This allows the polar response to be
more consistent as frequency increases, Fig. 16-99,
because the resistance in conjunction with the compli-
ance of the air inside the tube forms an acoustical

low-pass filter. High frequencies are attenuated at the

end of the tube because it is the high-resistance end,

PT

P T= 0 q

-------------------------

SL

O

sin ------u 1 – cosT

SL

O

------u 1 – cosT

= ----------------------------------------------------

Figure 16-95. Calculated frequency and phase response

curves of an interference tube microphone (250 mm)

without rear inlet for different angles of sound incidence.

Courtesy Sennheiser Electronic Corporation.

Figure 16-96. Calculated polar patterns of an interference

tube microphone (250 mm) without rear inlet. Courtesy

Sennheiser Electronic Corporation.

10

0

10

20

 30

0

90

180

270

360

100 200 500 1k 2k 5k 10k

o^0 o

o

o

0 o

o

o o

Frequency–Hz

Decibels