Correct option (c) 1.58 m
Explanation:
This is quarter wave matching. The length would be odd multiples of λ/4.
l = (2m + 1) λ/4
f1 = 429MHz
λ1/4 = (3 x 108)/(429 x 106 x 4)
l1 = 0.174m
f2 = 1GHz
λ2/4 = (3 x 108)/(109 x 4) = 0.075m
l2 = 0.075m
(2m + 1) = 1.58/l1 = 1.58/0.174 = 9
(2m + 1) = 1.58/l2 = 1.58/0.075 = 21
Only option (c) is odd multiples of both l1 and l2 .