PROPERTIES OF MATTER WAVES 49 



sound wave moving through air travels from its source and imparts an 

 energy to the receiver. This energy is primarily in the direction of propaga- 

 tion, but with scattering some of it becomes transverse. 



By contrast, the standing wave can impart no longitudinal energy — it has 

 none. But it can impart transverse energy to the medium. The generation 

 of the sound by the vibrating violin string is an example. 



The intensity, /, of the matter wave is the power delivered by it per unit 

 area. In. other words, / is the rate at which the wave expends energy. All 

 traveling waves move at a certain velocity, v (cm/sec). Hence the product of 

 amplitude (a pressure) times distance is the energy expended per unit area: 



w = \p d (dynes/cm 2 x cm = ergs/cm 2 ) 



The product of amplitude and velocity is the power expended per unit area: 



I = \p v (dynes/cm 2 x cm/ sec = ergs/cm 2 sec) 



The intensity or power expended per unit area by the traveling wave, is 

 highest for those media having molecules with the greatest number of de- 

 grees of freedom in which energy can be stored — gases for example. Both 

 the range and speed of sound are highest in solids, somewhat less in liquids, 

 far less in gases. However, for any medium of constant density, p, the ve- 

 locity has a fixed value. This fact results in another useful relationship, that 

 between amplitude (pressure) and intensity (power): 



/ = Vlvp 



which says simply that power delivered per unit area to any medium is pro- 

 portional to the pressure squared, if velocity and density are held constant.* 

 This (/ cc \^ 2 ) is a very useful rule-of-thumb, applicable, it turns out, to all 

 field phenomena. 



Useful also is the fact that, although low-frequency waves are easily re- 

 flected and diffracted by air and hence are nondirectional (or will go around 

 corners), high-frequency waves are only slightly scattered by air. Therefore, 

 the latter can be beamed in a preferred direction from a source, and even 

 focused on a particular spot by proper (saucer-like) design of the vibrating 

 source. 



*Dimensions: 



3 

 sec cm 



= ergs/cm sec 



(Work it through.) 



