230 Prof. A. Anderson : A/etlwd of finding Scalar and 

 Thus ,. satisfies the equation of wave-propagation. 



If A be any function of x 3 y, z, t that satisfies this equation 

 and F be any other function of x, y 9 z, t, then AF will also 

 satisfy the equation if 



\ox dx &y oy oz oz ) 



1 -, r 

 Let A be y and F any function of t . We have 



A?3F^aA 3F oA dF F' 



d# 3# By oy d~ oz c(r— f) 4LV bV by J 



and 



3F' 



F" r 2 F' rv \\ r 2 1 



c 2 (r-f)- <?'-f) 2 LV c/r~f *J 



fr-e' 



and thus 



\oa* o^ oy oy d^ oz J 



V oy 



iF'V 2 F' 



?^ + ?F - f? (^ + 2of, + ^). 



Also 



and 



BA 3F FV . 



?VF F'V 2 F' 



+zr«.(^+*)- 



o* 2 (r-f) a (r-f 

 Therefore 



?VF BA dF F'V 2 F' 



F K) 



Hence — - — = — satisfies the equation of wave-propagation, 



