48 



MATTER WAVES: SOUND AND ULTRASOUND 



matter waves the medium itself — solid, liquid, or gas — moves back and 

 forth. 



PROPERTIES OF MATTER WAVES 



Definition 



Matter waves are of two types, which differ only in the direction of the 

 vibration relative to the direction of propagation. In transverse waves the 

 vibration is perpendicular to the direction of propagation (a plucked violin 

 string, for example). In longitudinal waves the vibration is parallel to the 

 direction of propagation (the pressure waves from a blast, or in front of a 

 piston, for example). Most of the matter waves which are of interest here 

 are, like water waves, a combination of both. 



The two basic properties are the pressure (force/unit area) of the wave 

 and its rate of change with time. The former is usually called the ampli- 

 tude, \p (dynes/cm 2 ). The latter is usually expressed as the number of times 

 the value of \p cycles back and forth per second, i.e., as the frequency 

 (cycles/sec). 



All matter waves, no matter what the shape, can be expressed as a super- 

 position of simple, sinusoidal waves, of the type discussed in Chapter 1. 



There are traveling waves and standing waves (Figure 3-1 (a) and (b)). A 



<!> 



biost, 



shock, 



water waves 



auditory region (sound) 



ultrasonic region 



I 

 I 

 I 



'(b) 



I 



20 



21,000 



.000,000 



CYCLES PER SECOND 



Figure 3-1. (a) Traveling Wave Such as Sound in Air; Standing Wave Such as On a 

 Vibrating Violin String; (b) Range of Matter Waves. 



