50 MATTER WAVES: SOUND AND ULTRASOUND 



Illustrations 



Frequency 



Matter waves have a broad range of frequency, from zero up to the current 

 practical upper limit of about 1,000,000 cycles per sec (cps) in use in some 

 ultrasonic-therapy and submarine-detection studies (Figure 3-1 (c)). The 

 human ear is most sensitive from ^50 to ^10,000 cps; the range of man's 

 ear, however, may be from 20 to 21,000 cps. This, then, is the auditory or 

 sound range. Speech requires 60 to 500 cps. The piano ranges from 27.2 to 

 4138.4 cps. The great basso profondo, Italo Tajo, could reach a minimum of 

 ~60 cps; the diminutive coloratura soprano, Lili Pons, could hit 1300 cps on 

 a good day. Of course, these are the basic frequencies, and it is understood 

 that a basic frequency generated by any physical vibrator will contain over- 

 tones, or harmonics, which are multiples (2x, 4x, even 8x) of the basic 

 frequency. The quality of the tone is determined by the sum of all the com- 

 ponents: the basic frequency plus its harmonics. 



Training and youth combine to produce a receiver which can hear low- 

 power sound up to 12,000 cps. Some musicians can detect overtones from 

 their instruments up to 14,000 cps, but these are few. Most of us can detect 

 frequencies up to 18,000 from a signal generator, if the signal is intense 

 enough, and the odd person can detect up to 21,000 cps. Dogs do it with 

 ease. Porpoises have a phenomenal sonic system in their heads which can 

 sweep frequencies repetitively from a few cycles to many thousands of cycles 

 — both send and receive. 



Below and overlapping the auditory range for man is the range (0 to 50 

 cps) of blast and shock waves, earth tremors, water waves, and the like. The 

 masseur will use vibrations 1 to 50 cps; a ship will roll at 0.1 cps. An air 

 hammer operates at ~ 15 cps, and we hear the overtones. 



Above the range of sound, from 20,000 up to > 1,000,000, lies the im- 

 portant range of ultrasound, and the science and technology known as 

 ultrasonics. 



Velocity 



The speed of matter waves depends sharply upon the medium, and in the 

 case of a gas, its temperature and pressure. For instance, in air at 0°C and 

 1 atm pressure the speed is 331 meters/sec (mps) (730 miles/hr). In water 

 and soft tissue it is 4 1 2 times higher than in air, and in solids it goes up to 

 5000 mps. The velocity of sound through fat is 1440, through muscle 1570, 

 and through bone 3360 mps. 



Velocity is independent of frequency; and it is probably just as well, other- 

 wise the low tones of the organ might reach our ears later than the high 

 tones of the same chord! 



