194 



Tables 150-152 



TABLE 150. — Relative Strength of the Partials in Various Musical Instruments 



The values given are for tones of medium loudness. Individual tones vary greatly in quality and, 

 therefore, in loudness. 



TABLE 151. — Miscellaneous Sound Data 



Koenig's temperature coefficient for the frequency (») of forks is nearly the same for all pitches. 

 nt = « (i — o.ooonf" C), Ann. d. Phys. 9, p. 408, 1880. 



Vibration frequencies for continuous sound sensations are practically the same as for continuous light 

 sensation, 10 or more per second. Helmholtz' value of 32 per sec. may be taken as the flicker value for 

 the ear. Moving pictures use 16 or more per sec. For light the number varies with the intensity. 



The quality of a musical tone depends solely on the number and relative strength of its partials 

 (simple tones) and probably not at all on their phases. 



The wave lengths of sound issuing from a closed pipe of length L are 4L, 4L/3, 4L/5, etc., and from 

 an open pipe, 2L, 2L/2, 2L/3, etc. The end correction for a pipe with a flange is such that the antinode 

 is 0.82 x radius of pipe beyond the end; with no flange the correction is 0.57 x radius of pipe. 



The energy of a pure sine wave is proportional to n 2 A 2 ; the energy per cm 3 is on the average 

 2pTr 3 U 2 A 2 /X i \ the energy passing per sec. through 1 cm 2 perpendicular to direction of propagation is 

 2pTr 2 U 3 A 2 /\ 2 ; the pressure is £(y + 1) (average energy per cm 3 ); where n is the vibration number per 

 sec., X the wave length, A the amplitude, V the velocity of sound, p the density of the medium, 7 the 

 specific heat ratio. Altberg (Ann. d. Phys. 11, p. 405, 1903) measured sound-wave pressures of the 

 order of 0.24 dynes/cm 2 = 0.00018 mm Hg. 



TABLE 152. — Audibility as Dependent on Sound Pressure and Frequency 



The ear detects sounds over a pressure range about 0.001 to 1000 dynes/cm 2 ; over much of this 

 range it differentiates between complex sounds so nearly alike that no existing physical device can 

 distinguish them. Plot shows minimum audibility pressures from -j2 normal ears from 60 to 4000 cycles 

 (both scales logarithmic) ; standard deviation indicated by dotted curves. The maximum audibility curve 

 was obtained from 48 normal ears. A louder sound becomes painful. The intensity of pressure neces- 

 sary is about that required to excite the tactile nerves in the finger tips. (Wegel, Pr. Nat. Acad. Sc, 

 8, p. 155, 1922.) 



10000. 



1000. 



100. 



.001 



.0001 



Cycles per Secono 



10 20 50 100 200 500 1000 2000 5000 10000 20000 50000 



Smithsonian Tables 



