14 SOUND WAVES 



The particle velocity in this wave system from equations 1.11 and 

 1.46 is 



u = — = kJ [sin k{a — x) — sin k(a + x)] 1.49 



dx 



u = — Ik A [cos kct sin kx\ 1.50 



[sin {i 



u = ViA I sin \kct — -\ cos \kx — - 



1.51 



Equations 1.48 and 1.51 show that the maxima of the particle velocity 

 and pressure are separated by a quarter wavelength. The maxima of p 

 and u differ by 90° in time phase. 



A stationary wave system is produced by the reflection of a plane wave 

 by an infinite wall normal to the direction of propagation. This is the 

 simplest type of standing wave system. Complex stationary wave sys- 

 tems are produced when a sound source operates in a room due to the re- 

 flections from the walls, ceiling and floor. 



1.7. Sound Energy Density. — Sound energy density is the sound energy 

 per unit volume. The unit is the erg per cubic centimeter. 



The sound energy density in a plane wave is 



£ = — o 1.52 



where p = sound pressure, in dynes per square centimeter, 

 p = density, in grams per cubic centimeter, and 

 c = velocity of sound in centimeters per second. 

 The positive radiation pressure in dynes per square centimeter exerted 

 by sound waves upon an infinite wall is 



p = (y -\-l)E 1.53 



where E = energy density of the incident wave train in ergs per cubic 

 centimeter, and 

 7 = ratio of specific heats, 1.4 for air. 

 Instruments for measuring the radiation pressure have been built, con- 

 sisting of a light piston mounted in a large wall with means for measuring 

 the force on the piston. Since the radiation pressure is very small these 

 instruments must be quite delicate. 



1.8. Sound Intensity. — The sound intensity of a sound field in a speci- 

 fied direction at a point is the sound energy transmitted per unit of time 



