# Chapter 2 Summary

1. Sound propagation requires a material medium containing atoms or molecules. The atoms or molecules may be in the form of a fluid (such as a gas or liquid), a solid, or an interface between two of these phases of matter. Pressure is a measure of the degree to which the motions of atoms and molecules affect the motions of other nearby atoms and molecules.
2. Sound is the propagation of a perturbation in local pressure away from an initial location. It thus consists of alternating regions of higher-than-average pressure (molecular condensations) and lower-than-average pressure (molecular rarefactions).
3. Inside fluids, the molecules that pass on a pressure disturbance tend to move back and forth along the same axis on which the sound is propagating. The pattern of successive condensations and rarefactions moving away from the source of the disturbance is called a longitudinal wave. The molecules of a vibrating string propagate sounds along the string’s length, but they do so by vibrating on a line perpendicular to the direction in which the sound is propagating. This is called a transverse wave. The molecules on the surface of a body of water that is propagating ripples move elliptically and thus have both longitudinal and transverse components in their motion. Solids can also propagate sounds, but the molecules can move only tiny distances, if at all. Solids can support longitudinal and transverse waves, as well as a variety of elliptical and more complex patterns such as Rayleigh, Love, and bending waves.
4. A periodic wave repeats the pattern of pressure variation over time. The period of the wave is the amount of time (seconds) required to produce one complete cycle. The simplest type of periodic wave shows a sinusoidal pattern in pressure over time. The frequency of such a wave is equal to the number of times the pattern is repeated per second, and is measured in Hertz (abbreviated Hz). The part of the cycle that occurs at some reference time is called the phase of the wave. Finally, a wave’s deviations of pressure from ambient levels provide a measure of its amplitude. Amplitudes are usually measured on a logarithmic scale relative to some reference value. The units are called decibels (abbreviated dB).
5. Two waves of the same sinusoidal frequency passing through the same location are in phase if they have maxima and minima at the same time and out of phase otherwise. Waves that are in phase will show positive interference by creating a composite wave of similar frequency but enhanced amplitude; waves that are out of phase interfere negatively and tend to cancel each other out. Two sinusoidal waves that are similar but not identical in frequency will drift in and out of phase, creating beats.
6. Most animal sounds are periodic but not sinusoidal. In most cases, they can be decomposed into the sum of a set of pure sine waves (called a harmonic series) with frequencies that are integer multiples (called harmonics) of the lowest frequency in the set (called the fundamental). The decomposition (called Fourier analysis) can also be performed on aperiodic signals, but the sine wave components then tend to be more numerous, and their frequencies are not integer multiples of a single fundamental. Where the periodicity varies within animal sounds, one can usually break the sound into roughly periodic segments and perform a Fourier analysis on each segment. A plot of the Fourier decomposition of successive segments in an animal sound is called a spectrogram.
7. Inside fluids, all frequency components of a complex sound propagate at the same speed. In air, the speed of sound is about 344 m/sec (with variation depending on temperature and humidity). The speed of sound in water is about 4.4 times as fast as that in air, and the speed of sound in solids is about 15 times as fast as that in air. On the surface of a body of water and in certain solids, different frequency components may propagate at different speeds.
8. The spatial distance between the beginning and end of one cycle of a propagating sinusoidal wave is called its wavelength and is measured in meters. Wavelengths are inversely related to the wave frequency and directly related to the speed of sound in the medium. Wavelengths for a given frequency are thus longer in water than in air. Wavelengths may also be decreased, (and the effective frequency increased), if a sender and receiver are moving toward each other; wavelengths will increase if they are moving apart. This is called a Doppler shift.
9. Close to a sound source, medium molecules flow back and forth in unison. This is called the near field around the source. At distances of about 1/3 of the wavelength of the sound (or 2/3 the diameter of the source), medium molecules pass on the pressure disturbance without taking part in a cohesive tidal flow back and forth. The propagating medium at this and further distances from the source constitutes the far field of the sound.
10. Sound amplitudes decrease with distance from the source. Inside fluids such as water or air, the pressure of a sound radiating away from the source decreases with the reciprocal of the distance from the source. This is called spreading loss. Spreading losses are less severe for ripples on the water’s surface or inside the solid stems of plants. In addition to spreading losses, propagating high frequencies cause molecules to collide more often, and thus lose pressure to heat losses faster than propagating low frequencies. Spreading losses are the same in air and water, but heat losses are much higher in air.
11. Acoustic impedance is the resistance of a medium to a change in its molecular behavior. Away from interfaces between media, acoustic impedance depends on the density and speed of sound of that medium. Media with low acoustic impedances (e.g., air) propagate sound with weak pressures but significant molecular velocities; high-impedance media (e.g., water and solids) propagate sounds with high pressures and low molecular velocities. At an interface between two media with different acoustic impedances, most of the sound traveling in one medium will be reflected back into the same medium at the boundary. If the impedances are not too different, then some sound energy will pass into the second medium, but its direction of travel will likely be bent (refraction).
12. In addition to spreading and heat losses, a propagating sound can be attenuated by reflective scattering from objects that have acoustic impedances different from that of the medium, and by refraction that bends sound waves out of the path connecting sender and receiver.
13. Most animals produce sound signals in three steps: generation of vibrations, vibration modification, and coupling of the modified vibrations to the medium. Generation of vibrations can be achieved in many ways. Hard-bodied animals can use percussion (striking a body part against a substrate or another body part); stridulation (rubbing a file over a plectrum); buckling (of flat plates); or tremulation (vibrating the whole body on the surface of water or solid substrates). Animals in fluid media can also use pulsation, fanning, fluid compression, or streaming as vibrational sources. Finally, animals can force respiratory system air through openings to create aerodynamic vibrations in the form of hisses or single-frequency whistles, or through a valve like a glottis to create periodic but nonsinusoidal vibrations. Frogs, reptiles, and mammals have their vocalization valves in a larynx at the top of their trachea, whereas birds may have one valve at the bottom of the trachea (parrots and chickens), or a separate valve on each bronchus (songbirds, oilbirds, and woodpeckers). Wherever the bird valve is located, the associated tracheal-bronchial junction is called the syrinx. Birds with a valve on each bronchus can produce two different sounds at once, or more commonly, assign high frequencies to one valve and low frequencies to the other.
14. Modification usually involves linking the vibrational source to a flat surface or cavity with an acoustic impedance sufficiently different from the medium that successive vibrations overlap and can interfere. This facilitates positive interference and amplification (resonance), and negative interference (filtering) depending on the sound frequencies. High-Q modifiers provide strong amplification of a few select frequencies (normal modes), but have low damping that muddles rapid temporal patterning in the sound. Low-Q modifiers track temporal patterns accurately, but are much less selective for frequency and provide only minimal amplification.
15. Effective coupling of vibrations to the propagating medium depends in part on the size of the radiating surface, and in part on how it moves: monopoles expand and contract in all directions at once, dipoles oscillate along a single axis, and quadrupoles change shape by moving along two axes at the same time. Unlike monopoles, dipoles and quadrupoles produce directional sound fields. All three mechanisms are inefficient when the wavelengths of the radiated sounds are larger than the radiator, and the latter two are even more inefficient due to acoustic short-circuiting. These effects limit small animals communicating over moderate or greater distances to high frequencies. To create sufficiently high frequencies given limits on muscle contraction rates, small animals often resort to frequency multipliers. Examples include stridulation and vocalization mechanisms. Terrestrial animals can also improve radiation efficiency with acoustic horns or inflated sacs, which have acoustic impedances intermediate between that inside their bodies and that of the outside air.
16. Different species have evolved different compromises between elaborated sound structure and amplitude. Adaptations such as elongated tracheae in cranes and currasows, or cartilaginous vessels in ducks and howler monkeys, allow great amplitude at the cost of severely constraining what kinds of sounds can be produced and radiated. Species such as frogs, tree crickets, and mole crickets excavate or select calling sites that dramatically increase the resonance or radiation efficiency of the sounds they produce. Finally, species such as cardinals and humans actively vary the dimensions of their internal resonant cavities dynamically to amplify different frequency combinations during the production of a given sound.