(a) Creation of an acoustic shadow by an obstruction in the path of a sound wave; (b) absence of an acoustic shadow behind an obstruction when the sound wave is of low frequency (i.e. of a wavelength large relative to the size of the obstruction)

(a) Reflections from a parabola; (b) reflections from a convex surface; (c) reflections from a plane surface (after Parkin and Humphreys, 1958)

(a) Undesirable foci from an orchestra created by a concave reflector behind the platform; (b) undesirable focus created on a balcony by a concave ceiling; (c) undesirable focus created in a seating plan by a concave rear wall

Creation of an echo by (a) a reflector more than 13·5 m behind the source of sound; (b) a reflector more than 13·5 m behind the listener; (c) a difference in sound paths of more than 27 m; (d) flutter echo produced by sound reflected from two parallel surfaces

A small room (a) without reflectors, (b) with reflecting areas calculated on walls and ceiling, (c) with the addition of angled reflectors

(a) Geometrical construction used to determine the plane of a reflector in (c) and (d); (b) paths of direct sound, and several reflected sound waves in a 19th-century concert hall with traditional horizontal floor and ceiling and parallel side walls (the diagram illustrates the different types of reflection which aid listening in a concert hall; after Beranek, 1962); (c) plan of the seating (shaded) and stage, showing the complexity of the calculations necessary to determine the wall reflectors of a small auditorium; (d) shape of the floor and ceiling of same, showing the calculation for the ceiling reflectors (after Bagenal and Wood, 1931)

Diffusion produced by (a) a surface of concave reflectors of small radius, (b) a similar surface of convex reflectors, (c) a similar undulating surface

Sound waves, including all direct and reflected sound waves together as they are heard in a room of (a) long and (b) short reverberation time (RT); (c) effect of a long reverberation time (approximately 2·5 seconds) in the blurring of consecutive sounds in the opening bars of Beethoven’s Eighth Symphony; (d) increased clarity achieved in the same passage when played in a room with a short reverberation time (approximately 0·75 seconds)

(a) Section through a Helmholtz resonator; (b) axonometric section through a Helmholtz resonator panel; (c) axonometric section through a strip panel resonator

Plan of the theatre at Lyttos, Crete, showing the three rows each with 13 chambers for acoustic vases, as recorded by Onorio Belli, c1580 (from Hills, 1882)

Cross-sections of acoustic vases found in Swedish and Danish churches, with, on the left in each case, (a) front appearance in wall with block of wood inserted to constrict mouth of jar, (b) front appearance of pierced stone cover, (c) cross-section, to a small scale, showing positions in vault, (d) front appearance of positions in wall (after Brüel, 1947)

Examples of acoustic vases from medieval churches: (a) Youghal, Ireland; (b) Saint Laurent-en-Caux; (c) Fry; (d) St Peter Permountergate, Norwich; (e) St Olave’s, Chichester; (f) Denford; (g) Leeds, Kent; (h) Luppitt (after Hills, 1882)

Teatro alla Scala, Milan, 1778: (a) plan from George Saunders, ‘A Treatise on Theatres’ (London, 1790); (b) interior view: engraving by L. Cherbuin after Sidoli, early 19th century

Section of the Teatro Regio, Turin, 1740, as slightly amended in Pierre Patte, ‘Essai sur l’architecture théâtrale’ (Paris, 1782)

Section of the theatre at Besançon, designed by Claude-Nicolas Ledoux, 1776–83: engraving from M.H. Raval, ‘L’architecture considerée sous le rapport de l’art’ (1804)

Holywell Music Room, Oxford, opened 1748

Section of the Festspielhaus, Bayreuth, 1876: from Sachs and Woodrow, ‘Modern Opera Houses and Theatres’, i (1896)

Koussevitzky Music Shed, Tanglewood, Lenox, MA, 1959

Nodal patterns of modes 1, 2 and 5 in pairs of violin top and back plates ready for assembly

Geometry and approximate frequency positions of three body modes (B-1, B0, B1) and the two lowest cavity modes (A0, A1) of the finished violin

(a) Response curve showing the distribution and intensity of sounds produced by a violin when the force exerted on the bridge is simulated electronically; (b) loudness curve obtained on the same violin by bowing each semitone as loudly as possible

Measured directional characteristics of a violin in the plane through the bridge (after Meinel, 1957)

Radiation patterns of the violin (Meyer, 1972)

Shapes taken by a bowed string at a series of discrete points in time (solid lines) as the kink created at the point of bowing travels to the fixed end of the string and back once in every vibration, causing the optical illusion of a lenticular curve (dotted lines) (after Schelleng, 1974)

Sawtooth waveforms of string displacement produced by the alternate sticking and release of the rosined string by the rosined bow hair: (a) when bowed with a down-bow; (b) with an up-bow

Graph indicating the normal playing range for a bowed string instrument at constant bow velocity; the maximum and minimum bow force tend towards equality when the bow is very close to the bridge and diverge when it is further away (after Schelleng, 1974)

Wave shapes of force (not to be confused with those of displacement shown in fig.42) of a vibrating string on the bridge: (a) a bowed string; (b) a string plucked at its centre

Pressure response curves measured on an oboe for the air columns used in sounding the notes b′, f′ and b

First 12 modes of an ideal membrane: the mode designation (m, n) is given above each figure and the relative frequency below

Schematic representation of the generation of voiced sounds: the vibrations of the vocal folds generate a complex tone, the voice source, which has a uniform spectrum envelope tilt; voice source partials with frequencies corresponding to formant frequencies (such as the 2nd and 5th partials in the figure) are radiated with higher amplitudes than others

Diagram showing how the transglottal air flow varies with time in voiced sounds (the pitch perceived corresponds with the fundamental frequency, which is the inverse of the period time)

Tracings from X-ray pictures of the midsagittal contours of the vocal tract for the vowels indicated

Variations in the fundamental frequency in Hz (upper curve) and in the overall amplitude in dB (lower curve) in a vowel sung by a female singer; note that a rise in frequency is not necessarily accompanied by a rise in amplitude