F
REQUENCY ANDW
AVELENGTHThe frequency of sound vibration is the number of cycles of pressure change with respect to time. This is measured in units of cycles per second or Hertz (Hz) in the SI system. The human hearing sensation responds to frequencies between 16 Hz and about 20,000 Hz (Figure 2.1) while for other animals these limits are different (Figure 2.2) (Yost and Nielsen, 1985). For different insects the limits range between 15 Hz and 120 kHz (Roeder, 1965; Smith, 1979). The velocity of propagation is practically independent of the frequency for a very large range of frequencies extending up to more than 100 MHz. The wavelength though, being the distance covered by one
(a) (b) SPL(Nm−2) db Biological signal 200 140 Pain threshold 125 Jet Engine 20 120 115 Mole Cricket 105 Bushcricket 2 100 95 Field Cricket 0.2 80 75 Human speech 0.02 60 50 Drosophila 2×10−5 0 Hearing threshold 120 100 10−2 10−4 10−6 10−8 10−10 10−12 Threshold of feeling Threshold of hearing Frequency, Hz 100 80 60 40 Intensity level, decibels Intensity, Wm −2 20 20 100 1000 10,000 20,000 0.00002 0.0002 0.002 0.02 0.2 2 20 0
FIGURE 2.1 (a) Plot of human hearing limits as a function of frequency and (b) Measure of SPL for several sources. (Table from Ewing, A. W., Arthropod Bioacoustics: Neurobiology and Behaviour, Edinburgh University Press, Edinburgh, p. 260, 1989a. With permission.)
Insect Sounds and Communication: Physiology, Behaviour, Ecology and Evolution 12
cycle of the oscillation, depends on the velocity of the perturbation of the medium and therefore on the density of the medium. The relationship of this dependence can be explained as frequency ¼ velocity/wavelength:
f ¼n=l
In air, at mean sea level, the velocity of sound is 340 m/sec, so the wavelength of a 340 Hz oscillation will be 1 m, while if the oscillator emits at the frequency of 3.4 KHz, the wavelength will be 10 cm. In fresh water at 258C, the velocity of sound is 1493.2 m/sec, while in sea water it is 1,532.8 m/sec, giving wavelengths of 43 and 45 cm, respectively, it is for the same frequency of 3.4 kHz. In solids, the sound propagates with velocities varying from 6000 m/sec for the very dense granite to 1230 m/sec to the softer lead.
S
OUNDP
ROPAGATIONP
ROPERTIES:A
TTENUATION,N
EARF
IELDE
FFECTSAND
D
ISTORTIONA measure of amplitude of sound wave is given by the relative measure of sound pressure levels (SPL) with respect to a reference level:
SPL ¼ 20 log10ð p=prÞ in dB ðdecibelÞ units
where p is the measured pressure level and prthe reference pressure level. As pr¼ 2 £ 1025N/m2
which is the human hearing threshold at 4 kHz.
Sound level is dependent on the amplitude of the oscillation produced by the sound source, e.g. the vibrating diaphragm, and decreases with distance from the sound source. Since the perturbation of the sound wave is spreading radially in uniform space, sound intensity, which is the rate of energy transfer or energy flow at a given point, is inversely proportional to the distance from the source (Figure 2.3).
Sound intensity is also proportional to the product of pressure and particle velocity. As the wave propagates, apart from changes in pressure, the media particles also accelerate and decelerate. In fact at the source point, maximum pressure is exerted when the oscillating particles are at a
Drosophila Coleoptera Human voice Bird singing Cicadas Crickets Grasshoppers Bushcrickets Ants Lepidoptera Human Hearing 3.4m 10Hz 500Hz68cm. 34cm1kHz 68mm5kHz 10kHz34mm 6.8mm50kHz 100kHz3.3mm WavelengthFrequency
FIGURE 2.2 Frequency/wavelength ranges of various biological signals.
maximum distance from the equilibrium point. At the maximum distance of the particle from the equilibrium point, the velocity is zero and therefore the particle movement and pressure are 908 out of phase, while at a distance from the sound source this difference is diminished.
Since animals communicate in nonuniform media, modified by a large number of environmental factors, energy loss may be greater (Michelsen, 1985). In addition heterogeneities within the medium may cause scattering and interference effects, leading not only to sound damping, but also to directionality changes. If the medium through which the signal travels is not uniform, the signal will suffer some distortion as well as attenuation. The geometrical spreading which causes reduction of the pressure levels by half at doubling of the distance is further impeded by temperature and humidity (mainly in the air) changes (affecting the density) and heterogeneities of the medium.
Although particle movement is associated with pressure changes anywhere in the sound field, their directional components are most clearly experienced close to the sound source (near field). Recording sound with a conventional microphone close to a large radiating source at distances less than a third of the emitted wavelength will be affected by complex interferences. Since most insects use rather low frequencies for near field communication with wavelengths in air many times longer than that of the insect’s largest dimension, a pressure sensitive microphone is very inefficient for the detection of such signals. Detection would be better performed by particle movement sensors, such as ribbon microphones or systems with a light piezoelectric foil. For the detection of particle movement in solids, accelerometers and more recently laser vibrometers are used (see relevant Chapters 4, 5 and 22 in this book). The amplitude of particle displacement falls with the third power of the distance and because of this any near field effect will become almost insignificant at a distance of one or two wavelengths. This has important consequences for insects, many of which are small and produce low frequency sounds. Because acoustic efficiency is low at a distance of at least one wavelength (which in air for a frequency of 2 kHz is about 1.5 to 2.0 cm), for near field communication small insects use receptors to detect the particle velocity component rather than the pressure component (see Bennet-Clark, 1971). To be acoustically efficient insects must either be large or produce high frequency sounds.
Because the density and the elasticity of insect cuticles are very different from that of air, energy transfer to the surrounding medium is very inefficient. Thus in air, insects are rather inefficient at converting muscular energy to airborne sound. It is interesting that some insects produce signals with frequency components close to the resonant frequency of the sound propagating medium, diminishing the mechanical impedance and maximizing the vibration thereof. Efficiency increases to 23% in some beetles using substrate vibrations for communication (Leighton, 1987). High frequencies are attenuated more rapidly than low frequencies. So, the lower the frequency, the greater is the damping of the acoustic signal with distance. This also explains the nonuniformity of frequency components in signal detection with respect to distance (Michelsen et al., 1982).
Source A r 2r 3r 4A 9A Ω
FIGURE 2.3 Spherical spreading of a sound wave from a point source demonstrating the inverse square law attenuation of sound intensity.
Insect Sounds and Communication: Physiology, Behaviour, Ecology and Evolution 14
S
UBSTRATEV
IBRATIONSIn order to offset the inefficiency of air transmission, many insects use resonators to amplify sound. Others take the alternative route of producing substrate borne vibrations alone, at a much lower energy cost due to lower attenuation of mechanical energy in solids compared with air. The efficiency of an acoustic signal of a cricket is only 1% with respect to its muscular energy and for the cicada it is only 0.5% (Kavanach, 1987).
Most animals live on the interface of some solid with air or water and the waves which affect this interface will be significant for communication. Because of the nature of linear structures such as leaves and stems, vibratory information is transmitted as longitudinal, transverse and bending waves. Longitudinal and transverse waves will change with the length and width of the structure (e.g. stem), but bending waves will create changes along its surface.
Vibrations in solids are mainly transmitted as longitudinal waves (waves where the particle movement component is along the length of transmission), but their surface effects in the form of compression and extensions is less that 1% of total length. Transverse waves (waves where the particle movement component is perpendicular to the direction of wave transmission) produce an even less significant effect at the surface of the solid and are unlikely to be detectable. Bending waves are perturbations which are created in long, thin structures such as plant stems, where constructive interference of transverse waves can create amplified perturbation along the surface of the substrate. Because propagation velocity of bending waves depends on the physical properties and dimensions of the medium and the wavelength of the vibration, vibrations of different frequencies travel away from the sound source at different speeds. If the vibrations are in the form of pulses, which is something usual in insect communication, their group propagation velocity is twice the phase velocity.
Since the information collected by insect receptors concerns the relative movement at the surface of the substrate, measurements taken from accelerometers (instruments used to measure surface
vibration), given as a rate of change (m/sec2), relate to the amplitude with which a portion of the
substrate rises and falls. For low intensity bending waves, amplitude will be low and vertical vibration velocity will be small. For more intense vibrations, surface vibration velocities will be high.
S
IGNALS
TRUCTURE ANDT
ERMINOLOGYIn order to compare signals emitted from the same individual, in different conditions or different individuals of the same or different species, certain terminologies have been adopted to describe the hierarchical structure. Calling songs are repeated over long periods of time. The repeat is sometimes called a phrase. Each repeatable phrase usually consists of two subgroups with strong amplitude variations, followed by a silent interphase gap (ICD). The two subgroups of the phrase are referred as low amplitude (LPD) and high amplitude (HPD) parts (Sueur and Aubin, 2004). In the temporal domain, there is big variation in the frequency of phrases (phrases per second), but for most acoustic signals the phrases last for periods of seconds. Each phrase subgroup consists of chirps or echemes with a temporal length of the order of hundredths of seconds or some tenths of milliseconds (msec). In more detail each echeme has an internal structure of syllables which are of the order of milliseconds. Further, these consist of pure pulses or impulses of the order of tenths of milliseconds. Impulses normally represent the principal unit of sound or vibration production, such as a wing flick, a single tooth strike or a leg movement (Figure 2.4).