The following equations represent transverse waves :
`z_(1) = A cos(kx - omegat)`,
`z_(2) = A cos (kx + omegat)`, `z_(3) = A cos (ky - omegat)`
Identify the combination (s) of the waves which will produce (i) standing wave(s), (ii) a wave travelling in the direction making an angle of `45^(@)` with the positive `x` and positive `y` axes. In each case, find the positions at which the resultant is always zero.

Answer

(i) `z_(2)&z_(2),x=((2n+1)pi)/(2k)` where n=0,1,2,3,. . .
(ii) `z_(1)&z_(3),(x-y)=((2n+1))/(k)pi` where n=0,1,2, . . .

Explanation

(i) `z_(1)&z_(2),x=((2n+1)pi)/(2k)` where n=0,1,2,..
(ii) `z_(1)&z_(3),(x-y)=((2n+1))/(k)pi`where n=0,1,2, . ..