A.— MATHEMATICAL AND PHYSICAL SCIENCES 33 



by the ear) with the associated energy, which can be quantitatively 

 measured by physical instruments. 



Let us first consider the measurement of acoustical energy. For the 

 purpose, we need an intensity meter, this commonly consisting of a 

 microphone and amplifier together with a suitable rectifier and indicator. 

 Moving-coil or ribbon microphones are sometimes employed, though for 

 fundamental work the condenser or the crystal microphone is preferred 

 despite the lower sensitivity. Whatever the microphone used, it is 

 usually calibrated by direct interchange comparison under appropriate 

 conditions with a standard (pressure) microphone of the condenser type 

 which in turn has been fundamentally calibrated in absolute units by 

 means of either the Rayleigh disc or the pistonphone. 



The Rayleigh disc depends for its operation on the tendency of a small 

 thin glass disc suspended from its edge by a fine fibre to set itself at right 

 angles to a sound field. The torsional constants of the system and the 

 degree of deflection of the disc aflford the sound particle velocity, the 

 corresponding sound pressure being calculable from the known relations 

 in the field. The measurements are made either in a stationary- wave 

 pipe or in a room with highly absorbent walls. 



The piston-phone, which measures sound pressures directly, consists 

 essentially of a small cavity, one face of which is closed by the diaphragm 

 of the standard microphone, the opposite face consisting of a small piston 

 connected to the moving coil of a loudspeaker unit. The amplitude of 

 motion of the piston, when it is set in vibration, is measured optically 

 and enables the corresponding sound pressures in the cavity to be 

 calculated. 



So much for intensity measurements. As regards the associated 

 loudness levels, we turn to auditory diagrams of the ear, such as those of 

 Fletcher and Munson (1933). The various loudness contours for pure 

 tones of diff'erent frequencies show that while loudness and energy are 

 manifestly related, the two do not normally keep in step, particularly 

 for notes of very high and very low frequencies. At feeble intensities, 

 the ear exercises pronounced selective preference for notes of medium 

 frequency and it is only at high intensities that equal increments of 

 energy produce even approximately equal increments of loudness. 

 Furthermore, the thresholds of hearing are much higher for high and low 

 frequencies, so that the corresponding ranges of intensity with which the 

 ear can deal, are more restricted than for notes of medium frequency. 

 The situation is worsened in the case of complex sounds or noises 

 since the loudness is aff'ected by their character, there being in general 

 no simple relation between the loudness of a noise and the energy- 

 loudness characteristics of its several components. It is evident that 

 an energy meter, such as a microphone system, cannot unreservedly be 

 used as a direct measurer of loudness. 



The Decibel and the Phon, 

 The next step in the measurement of noise is to equip ourselves with 

 units and standards of loudness. In this connection, we have to cater for 

 the enormous intensity range of the ear, particularly for notes of medium 



