acoustics

acoustics. In its true sense, anything pertaining to the sense of hearing, but, as commonly used, firstly, the branch of physics concerned with the properties, production, and transmission of sound; and secondly, the quality of a building as regards its suitability for the clear hearing of speech or mus.

Sound is due to the vibrations of a source, such as a mus. instr., which are transmitted through the air to the ear-drum where they set up vibrations at the same rate. The pitch of a sound depends on the speed of those vibrations, which if rapid produce a ‘high’ pitch and if slow a ‘low’ pitch. The rate of vibration per second is known as the ‘frequency’ of the note.

The loudness of a sound depends on the ‘amplitude’ of the vibrations; for instance, a vn. str. violently bowed will oscillate for a considerable distance on either side of its line of repose, thereby producing strong vibrations and a loud sound, whereas one gently bowed will only oscillate a short distance on each side and so produce small vibrations and a soft sound.

Smaller instr. produce more rapid vibrations and larger ones slower vibrations: thus the ob. is pitched higher than its relative the bn., likewise a vn. than a vc., a stopped str. than an ‘open’ str., a boy's v. than a man's v., etc. But other factors enter into the control of pitch. For instance, mass (the thinner str. of a vn. vibrate more quickly than the thicker ones and so possess a higher general pitch) and tension (a vn. str. tightened by turning the peg rises in pitch).

The varying quality of the sound produced by different instr. and vv. is explained as follows. Almost all vibrations are compound, e.g. a sounding vn. str. may be vibrating not only as a whole but also at the same time in various fractions which produce notes according to their varying lengths. These notes are not easily identifiable by the ear but are nevertheless present as factors in the tonal ens. Taking any particular note of the harmonic series (as G, D, or B), the numbers of its harmonics double with each octave as the series ascends. The numbers attached to the harmonics represent also the ratios of the frequencies of the various harmonics to the fundamental. Thus if the frequency of the low G is 96 vibrations per second, that of the B in the treble stave (5th harmonic) is 5×96 = 480 vibrations per second.

Whilst these harmonics are normally heard in combination some of them may, on some instr., be separately obtained. By a certain method of blowing, a brass tube, instead of producing its first harmonic, or fundamental, can be made to produce other harmonics. By lightly touching a str. (i.e. a stopped str.), at its centre and then bowing it, it can be made to produce (in a peculiar silvery tone-quality) its 2nd harmonic; by touching it at a 3rd of its length it will similarly produce its 3rd harmonic, etc. (Harmonics are notated in str. parts as an ‘o’ above the note. ‘Natural’ harmonics are those produced from an open str.; ‘artificial’ harmonics those produced from a stopped str.)

The normal transmission of sound is through the air. The vibrations of a str., a drum-head, the vocal cords, etc. set up similar vibrations in the nearest particles of air; these communicate them to other particles, and so on, until the initial energy is gradually exhausted. This process of transmission of pressure to adjacent units of air creates what are known as sound waves: unlike waves created by water-motion, there is no forward movement, but each particle of air oscillates, setting up alternate pressure and relaxation of pressure which in turn produce similar effects on the human or animal eardrum (= vibrations), so causing the subjective effect of ‘sound’.

To judge pitch differences, or intervals, the human ear obeys a law of perception called the Weber–Fechner law, which states that equal increments of perception are associated with equal ratios of stimulus. Perception of the octave pitch is a 2:1 frequency ratio. In judging the loudness of sound there are 2 ‘thresholds’, those of hearing and of pain. If the intensity of sound at the threshold of hearing is regarded as 1, the intensity at the pain threshold is 1 million million. Acousticians' scale of loudness, following the Weber-Fechner law, is logarithmic and based on a ratio of intensities 10:1. This is known as a bel. The range of loudness perception is divided into 12 large units. Each increment of a bel is divided into 10 smaller increments known as decibels, i.e. 1 bel = 10 decibels. A difference in loudness of 1 decibel in the middle range of hearing is about the smallest increment of change which the ear can gauge.

When 2 notes near to one another in vibration frequency are heard together their vibrations necessarily coincide at regular intervals and thus reinforce one another in the effect produced.

This is called a beat. When the pf. tuner is tuning a str. of a certain note to another str. of the same note the beat may be heard to diminish in frequency until it gradually disappears with correct adjustment. When the rate of beating exceeds 20 per second, the sensation of a low bass note is perceived.

When 2 loud notes are heard together they give rise to a 3rd sound, a combination or resultant tone, corresponding to the difference between the 2 vibration numbers: this low-pitched note is called a difference tone. They also give rise to a 4th sound (another combination tone—high and faint) corresponding to the sum of the 2 vibration numbers: this is called a summation tone.

There is reflection of sound, as of light, as we experience on hearing an echo. Similarly there are sound shadows, caused by some obstruction which impedes the passage of vibrations which reach it. However, unlike light vibrations, sound vibrations tend to ‘diffract’ round an obstruction, and not every solid object will create a complete ‘shadow’: most solids will transmit sound vibrations to a greater or lesser extent, whereas only a few (e.g. glass) will transmit light vibrations.

The term resonance is applied to the response of an object to the sound of a given note, i.e. its taking up the vibrations of that note. Thus if 2 identical tuning-forks are placed in close proximity and one is sounded, the other will set up sympathetic vibrations and will also produce the note. The 1st fork is then a generator of sound and the 2nd a resonator. It is often found that a particular church window will vibrate in response to a particular organ note, and that a metal or glass object in a room will similarly respond to a certain vocal or instr. note.

This phenomenon is true resonance (‘re-sounding’) in the strict scientific sense of the word. There is also a less strict use of the word, which is sometimes applied to the vibration of floor, walls, and ceiling of a hall, not limited to a particular note, but in response to any note played or sung. A hall may either be too resonant for the comfort of performers and audience, or too little so—too ‘dead’ (a hall with echo is often described as ‘too resonant’, but there is an obvious clear distinction to be made between the mere reflection of sounds and the sympathetic reinforcements of them). Reverberation time is defined as the time it takes for sound to fall 60 decibels (1 millionth of original intensity).

Materials of walls and ceiling should be neither too reverberatory nor too absorbent (‘dead’). Acoustical engineers have worked out co-efficients of absorption for building materials, but absorption is rarely uniform throughout the whole spectrum of pitch. Only wood and certain special acoustic materials show nearly even absorption in the total frequency range. Amplifiers and loudspeakers can be used (as they nowadays often are) to overcome difficulties caused by original faulty design. Most modern halls can be electronically ‘tuned’ and have movable panels, canopies, and reverberation chambers which can be adapted to whatever type of music is being performed.