24 Mr. Holmes on 



of a progressive and partly of a retrograde wave, of which 

 the amplitude of the former is 



-J'ii 





sm^viftzY^j 



while that of the latter is 



^V I) 



cotQsmv7nz. 



We will now show that the solution given satisfies the 

 equation of energy. In the wave 



^ = Hcos(;2/ - inx) 

 the work transmitted across unit area in time t is 



W = -D,-HV. 



2 ??l 



We will now obtain the expression for the work transmitted 

 across unit area in time t, in the wave 



-v^-{ 



. \ co^vmzcos{nf - inx) - . sm{nt - inx) + cotO 

 If P be the pressure and IV the variation of pressure 



= iH^D,^' jcosV;;/^ + sinV^^ _ cot^Osin^r;^^ + 



.... periodic terms \ 



^H^Do- \ I + periodic terms 

 2 ;;/ (^ 



2 



2 ;;/ 



which shows that the condition of energy is satisfied. 



Let us now consider the value of the small quantity 

 J^ and show that it is less than 4. 



We have 



mK. 27rK 

 where v is the velocity of sound 7 is 1-410. 



