266 MEASUREMENTS 



power transmitted through the incremental areas and may be expressed as 



Pa = - fJp^dS X 10-7 11.11 



where Pa = total acoustic power, in watts, 



p = density of the medium, in grams per cubic centimeter. 

 c = velocity of sound in medium, in centimeters per second, 

 p = root-mean-square pressure, in dynes per square centimeter, 

 over the element of areas dS, and 

 dS = element of area on spherical surface, in square centimeters. 

 The input power can be determined in the obvious manner while oper- 

 ating under the above conditions. 

 The efficiency /jl in per cent is then 



^ = — i X 100 11.12 



Pe 



where Pa = total acoustic output, in watts, and 

 Pe = electrical input, in watts. 



As previously mentioned, the loud speaker should be located so that 

 the reflected energy reaching the measuring equipment is negligible. 

 This means that the measurements must either be made in a room with 

 totally absorbing walls or in free space. The measurements and compu- 

 tations in this method are quite laborious. On the other hand, there can 

 be no question as to the validity of the results which are obtained if the 

 test is carefully conducted. Because of its fundamental nature and 

 validity, the direct method is usually considered standard for determining 

 loud speaker efficiency. 



2. Indirect Determination of Radiated Power. — There are several 

 methods for determining loud speaker efficiency by indirect means. The 

 most common method is to measure the electrical impedance under va- 

 rious conditions of diaphragm loading. 



A one-to-one ratio bridge, capable of measuring the impedance at the 

 full power output of the speaker, should be used. Care should be taken 

 that the temperature of the voice coil does not vary appreciably during 

 the various measurements. The power supply for driving the speaker and 

 bridge should be reasonably free from harmonic distortion. 



The motional impedance method ^^ is generally applied to moving coil 

 electrodynamic speakers in which the force factor is real. In case the force 



28 Kennelly and Pierce, Proc, A. A. A. S., Vol. 48, No. 6, 1912. 



