The modulation frequency of an AM radio station is 250 kHz , which is 10% of the carrier wave. If another AM station approaches you for license, what broadcast frequency will you allot?

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2000 KHz

2250 KHz

2900 KHz

2750 KHz

answer is A.

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Detailed Solution

$G i v e n, f_{m} = 250 K H z A n d a l s o t h a t f_{m} i s 10 % o f f_{c}, i . e f_{c} = 2500 K H z N o w, F o r a g i v e n c a r r i e r w a v e o f f r e q u e n c y w i t h m o d u l a t i o n f r e q u e n c y f_{m}, t h e b a n d w i d t h i s c a l c u l a t e d b y f_{u p p e r} = f_{c} + f_{m} f_{l o w e r} = f_{c} - f_{m} T o a v o i d o v e r l a p p i n g o f b a n d w i d t h s, n e t b r o a d c a s t f r e q u e n c i e s c a n b e f_{1} = f_{c} \pm 2 f_{m}, f_{2} = f_{c} \pm 3 f_{m} S o n e x t i m m e d i a t e a v a i l a b l e b r o a d c a s t f r e q u e n c y i s f_{1} = f_{c} + 2 f_{m} = 2500 + (2 \times 250) = 3000 K H z a n d f_{1}' = f_{c} - 2 f_{m} = 2500 - (2 \times 250) = 2000 K H z$