Transmission Parameters of an Audio-Rate Frequency Modulated Sound of a
Female Mosquito
Maweu O. M, Muia L. M, Deng A. L*.
Physics department, Egerton University, P.O.box 536, Egerton, Kenya.
*
Zoology department.
E-mail. mawmant@yahoo.com
Key words: Audio spectra, Anopheles gambiae, modulating index, resonant frequency,
carrier frequency
Abstract
This work has established the modulating frequency (intelligence) to be at 97.7 Hz for all
the species of mosquitoes studied, namely; Culex pippen, Anopheles gambiae and Aedes
egypti. The signal carrier frequency is 488.3 Hz for all the species, except the medically
important Anopheles gambiae which is at 293 Hz. Bessel functions were used to
determine the number of audio side bands or the bandwidth (BW). The bandwidth for the
medically important Anopheles gambiae was found to be 781.6 Hz. The first order
sidebands (  f1 ), that is, (97.7) were found to be the resonant frequencies occurring at
95.4 Hz and 390.6 Hz respectively, with an amplitude of 9.57 mV. Other species, i.e.
Aedes egypti and a 'swarm' had a bandwidth of 1.36 kHz with resonant frequencies
occurring at the second order sidebands (  f 2 ,) or, 293 and 683.6 Hz with an amplitude
1
of 10.22 mV. The limits of the operational band created by the resonant frequencies
enable the males to identify females of their kind.
Introduction
Mosquitoes communicate with each other, specifically for mating purposes.
These insects produce sound when in search of proteins needed for ovulation. Since these
waves are frequency modulated, Baker (1979), it is necessary to establish the
transmission parameters associated with the intelligence of the signal, since it has the
message the insect is transmitting. The range of frequencies generated by these insects is
between 150 Hz and 500 Hz, Ewing (1989).
This is basically the carrier frequency. The sound of a female mosquito in-flight
is transmitted in air as a frequency modulated wave (FM), Baker (1979). These are
normally low frequency waves referred to as classic or Chowning frequency modulation.
Simple Chowning FM uses the sine wave, which produces no other frequencies apart
from its fundamental, as both the carrier and the modulating waveform, Chowning
(1973). These frequencies are associated with long wavelengths in the range of meters,
and little is known of the insects' response to these wavelengths in the electromagnetic
spectrum, Baker (1979).
The aim of this study was to analyze the audio spectrum of a female mosquito
in-flight and determine the transmission parameters, namely the amplitude, carrier
frequency ( f c ), modulating frequency ( f m ), modulating index, ( m f ) frequency deviation
(  ), bandwidth (BW) and the wavelength (  ).
2
The formation of the spectrum is due to the modulating frequency being at the audio rate,
Chowning (1973). The spectrum contains the fundamental frequency, representing the
carrier frequency and side bands occurring on either side of the carrier.
For a frequency-modulated wave, the equation for instantaneous voltage may be written,
Muller (1978),
e  A sin  i  m f sin  c 
(1)
Where A is the peak value of the carrier wave
 c is the carrier angular frequency
 m is the modulating signal angular frequency and
mf 

fc
is the modulation index.
The solution of (1) is given by
f c (t )  J 0 (m f ) cos ct  J (m f )[cos(c  i )t  cos(c  i )t  J 2 (m f )
[cos(c  2i )t  cos(c  2i )t ]
(2)
Where J n (m) is the Bessel function of the order n
f c (t ) Is the modulated frequency component.
J 0 (m f ) cos t Is the carrier frequency component.
J1 (m f )[cos( c  cos i )t  (cos  c  cos  i )]t is the component at  f i (sideband)
J 2 (m f )[cos( c  2 i )t  (cos  c  2 cos  i )t ] is the component at  2 f i around the
carrier, etc.
Amplitude for the side band component Jn were obtained using the standard expansion
for Bessel functions namely;
3
mf
mf
mf
( )2
( )4
( )6
1
2
2
J n (m f )  ( ) 2 [  2


   ]
2
n! 1!(n  1)! 2!(n  2)! 3!(n  3)!
mf
(3)
Experimental
Capture of mosquitoes and recording of the sounds
In practice, it is very difficult to tape the sound of a mosquito in-flight in an open
room. Thus, captive and disease free mosquitoes obtained from a research institute
(Kenya Pyrethrum-Board) were left unfed for a day. A single mosquito of each species
was enclosed in a small mesh cage (12 cm 3 ). An attractant was placed near the cage to
ensure that the mosquito made continuous flights in search of food. The sound emitted by
the mosquito was then recorded on a magnetic tape using a cord-less microphone.
Later a combination of all the species was put in the cage to form a ‘swarm’ and their
sounds recorded. The taped audio signals were transferred to a fluke view combi-scope
through a butter-worth filter to eliminate all the frequencies above 700 Hz, Millman and
Halkias (1983). The scope was set to auto-mode so as to capture the actual signal
strength.
Generation of the FM spectrum
Fluke-View combi-scope proprietary software , Fluke view cooperation (1995)
was used to transfer the data from the scope to a computer. Care was taken when
selecting the baud rate to ensure that sufficient data points were transferred to the
computer so as to obtain a good frequency spectrum. Fourier transforms were performed
on the spectrum to extract the basic transmission parameters such as the fundamental and
the side frequencies.
4
Results and Discussion
The frequency modulated (FM) sidebands were calculated from equation (3)
using standard values of Table 1, while Figure 1 shows the frequency spectrum for the
medically important Anopheles gambiae.
Scanning the spectrum (Fig.1) from either side of the zero position gives the side bands.
The zero position represents the fundamental component as the carrier, with amplitude of
4.31 mV and a frequency of 293.4 Hz. This is designated as J0 in Table.2. Besides the
fundamental component are eight side bands. The first order side bands (  f1 ) has
amplitude of 9.57 mV. The second order side bands (  f 2 ) has amplitude of 3.67 mV, the
third order (  f3 ) is 0.9 mV and the last significant pair has an amplitude of 0.09 mV.
The next pair with amplitude of 0.05 mV is not transmitted
Other important parameters, i.e. frequency deviation, modulating index, band width
and the transmitting wavelength obtained from the spectra data were as below [6];
(1) Frequency deviation (  ) = 488.3 - 293 = 195.3 Hz
(2) The modulating index ( m f ) =
195.3

 1.9
=
97.7
fm
(3) Bandwidth (BW) = 2  n  f m
2  4  97.7  781.6 Hz.
(4) Wavelength ( ) =
340
v
 1.16m
=
293
fc
Where v is the velocity of sound in air and f c is the carrier frequency.
With 195 Hz deviation and a 97.7 Hz audio, the ratio of modulation index to the
deviation is 1.9. With this modulation index, four significant pairs of sidebands were
5
developed. These are shown in Figure 1. The least significant sideband from the carrier is
4  97.7Hz or 390.6 Hz, producing a total side bandwidth of 781.6 Hz. It is unlikely that
any signal of amplitude less than 0.1 mV will be transmitted.
Table 2 is the interpretation of the spectrum of Fig.1 in terms of frequencies. Here J0 is
the carrier whose position in the spectrum is zero, with frequency 293.4 Hz. While  J1
denotes the first side bands occupying the position from – 98 to + 97.7 on either side of
the carrier in the spectrum. Their frequencies are 195.5 and 390.4 Hz.
Figure 2 shows a frequency spectrum of Culex pippen. The fundamental
component has amplitude of 6.45 mV at a carrier frequency of 488.3 Hz. This is shown in
Table 3, which is the interpretation of Figure 2. On either side of the fundamental are
seven sidebands, implying fourteen sidebands, extending the bandwidth to 1.36 KHz. The
first pair of side bands has amplitude of 7.45 mV. It is unlikely that all the components of
the bandwidth will transmit due to their low amplitudes as can be seen from the figure.
The transmitting parameters can be calculated from this spectrum as follows;
(1) Frequency deviation (  ) = 488.3 - 97.7 = 390.6 Hz
(2) Modulating index ( m f ) = 3.9
(3) Band width (BW) = 2  7  97.7  1.36 KHz
(4) Wave-length (  ) =
340
 0.87 m .
390.5
Table 4 is the summary of the transmission parameters of the species of mosquitoes
studied.
Results have shown that different species of mosquitoes have different resonant
frequencies despite having the same modulating frequencies. The spectrum of Anopheles
6
gambiae has a narrow band of 781.6 Hz width compared to Aedes egypti which is 1.36
KHz.
For, if n is the number of audio or significant pairs of frequencies, then
BW
n

2
mf
(4)
Predicts the ratio of the bandwidth to the total deviation depending for a given
modulating index m f . For m f > 1, the ratio tends to unity and the bandwidth is almost
equal to or slightly larger than 2  ,Gupta (1966). This is true for the cases of Anopheles
and Aedes, and the ‘swarm’. For harmonic spectra, the carrier is not necessarily the
fundamental frequency. For the carrier to be the fundamental, it must be at least equal to
twice the modulating frequency , Hass (2001). In the spectra studied, the carrier
frequency is in all cases satisfied this condition. We therefore, can treat the carrier as the
fundamental frequency. In this case, the spacing between the fundamental and the nearest
side band gives the modulating frequency, Shrader (1993).
Conclusions
From the foregoing and Table 4, mosquitoes use both direct and indirect method
of FM generation, i.e., the Armstrong type of FM generation, in which phase modulation
is used to generate frequency modulation, Muller (1978) for communication. This is
evident from the high value of the modulation index, which are 3.9. Under these
conditions, the Bessel function introduces a phase reversal to the carrier. Further, the
narrow bandwidth, which is a few hertz, is a characteristic of communication bandwidths,
Muller (1978). For mosquitoes, the bandwidth is the range that contains all the frequency
components that are audible to the human ear. The occurrence of the resonant frequencies
7
at 195 and 390.6 Hz for the Anopheles gambiae and at 293.6 and 683.6 Hz for other
species is consistent with the range of frequencies obtained from Bioacoustics which is
between 150 and 650 Hz, Ewing (1989). Mosquitoes emit sounds for the purpose of
mating and feeding in the frequency range 97.7 Hz to 684.6 Hz depending on the species.
The mode of intelligence transmission is through frequency modulation at a carrier
frequency of 293 Hz, modulating frequency ( f m ) of 97.7 Hz and modulating index of 1.9
( m f ) for the Anopheles. On the other hand, Aedes egypti and culex pippen transmit at a
carrier frequency of 488.3 Hz, modulating frequency m f of 97.7 Hz and modulating
index of 3.9.
References
Baker G, 1979. Magnetic influence on the activity of termites and their
directional behavior in building vertical galleries. mater.org. 14 : 534-548.
Chowning J, 1973. The synthesis of complex audio spectra by means of
frequency modulation. Journal of audio engineering society, 21: 7.
Clement A. N, 1992. Biology of mosquitoes, (Chapman and Hall, U.K.), Pp ixxii.
Ewing A.W, 1989. Anthropod Bioacoustics, (Edinburgh university press,
U.K.), Pp 62.
Fluke view combiscope soft ware for windows, 1995. (Fluke Corporation,
U.S.A.)
Gupta K, 1966. Hand book of electronics, (Pragati and Prakash publishers,
India), Pp 1445-1475.
Hass J, 2001. Center for electronic and computer music, (Indiana university,
8
USA).
Millman J and Halkias C, 1983. Integrated electronics, (Tata McGraw-Hill, New
Delhi), P p 875.
Muller G.M, 1978. Modern electronic communications, (Prentice-Hall
International, U.K.), Pp 158-170.
Shrader R. L, 1993. Electronic communication, (Macmillan McGraw-hill,
IIinois), Pp. 355-433.
9
Table 1. FM sidebands
(m f )
J0
J1
J2
J3
J4
J5
J6
0.00
1.0
0.25
0.98
0.12
0.5
0.94
0.24
0.03
1.0
0.77
0.44
0.11
0.02
1.5
0.51
0.56
0.23
0.06
0.01
2.0
0.22
0.58
0.35
0.13
0.03
2.5
-0.05
0.50
0.45
0.22
0.07
0.02
3.0
-0.26
0.34
0.49
0.31
0.31
0.04
0.01
4.0
-0.40
-0.07
0.36
0.43
0.28
0.13
0.05
J7
0.02
Table 2. Side Bands from the audio spectrum of Anopheles gambiae
J0
J1
J2
 97.7 Hz
293.4 Hz
J3
 195.4 Hz
J4
 370.6 Hz
 488.3 Hz
Table 3 Side bands from the audio spectrum of Aedes egypti and a ‘swarm’
J0
488.3 Hz
J1
 97.7
J2
J3
J4
J5
J6
J7
 195.4
 293.4
 390.6
 685.7
 685.7
 781.6
Table 4 Summary of transmission wave parameters of mosquitoes
Species
fc
BW
Anopheles
293 Hz
781.6
Others
488.3 Hz
1.3 kHz

Hz
195.3
Hz
390.4 Hz
10

mf
n
1.16 m
1.9
8
0.87 m
3.9
14
Figure 4.1 Frequency spectrum of Anopheles gambiae
12
Amplitude [mV]
10
8
6
4
2
390
288
195
97.7
0
-98
-195
-288
-391
0
Frequency [Hz]
Figure 2 Frequency spectrum of Aedes egypti
12
8
6
4
2
Frequency [Hz]
11
685
489
288
97.7
-98
-288
-489
0
-685
Amplitude [mV]
10