LOUDNESS 381 



reference or zero for loudness levels. In many ways the threshold of 

 hearing intensity for a lOOO-cycle tone seems a logical choice. How- 

 ever, variations in this threshold intensity arise depending upon the 

 individual, his age, the manner of listening, the method of presenting 

 the tone to the listener, etc. For this reason no attempt was made to 

 choose the reference intensity as equal to the average threshold of a 

 given group listening in a prescribed way. Rather, an intensity of the 

 reference tone in air of 10~^^ watts per square centimeter was chosen 

 as the reference intensity because it was a simple number which was 

 convenient as a reference for computation work, and at the same 

 time it is in the range of threshold measurements obtained when 

 listening in the standard method described above. This reference 

 intensity corresponds to the threshold intensity of an observer who 

 might be designated a reference observer. An examination of a large 

 series of measurements on the threshold of hearing indicates that such 

 a reference observer has a hearing which is slightly more acute than 

 the average of a large group. For those who have been thinking in 

 terms of microw^atts it is easy to remember that this reference level is 

 100 db below one microwatt per square centimeter. When using these 

 definitions the intensity level /3r of the reference tone is the same as its 

 loudness level L and is given by 



^, = L = 10 log /. + 100, (3) 



where Jr is its sound intensity in microwatts per square centimeter. 

 The intensity level of any other sound is given by 



/3 = 10 log / + 100, (4) 



where / is its sound intensity, but the loudness level of such a sound 

 is a complicated function of the intensities and frequencies of its 

 components. However, it will be seen from the experimental data 

 given later that for a considerable range of frequencies and intensities 

 the intensity level and loudness level for pure tones are approximately 

 equal. 



With the reference levels adopted here, all values of loudness level 

 which are positive indicate a sound which can be heard by the reference 

 observer and those which are negative indicate a sound which cannot 

 be heard by such an observer. 



It is frequently more convenient to use two matched head receivers 

 for introducing the reference tone into the two ears. This can be done 

 provided they are calibrated against the condition described above. 

 This consists in finding by a series of listening tests by a number of 



