In a broadcast transmitter, the RF output is represented

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In a broadcast transmitter, the RF output is represented as
e(t) = 50 [1 + 0·89 cos 5000 t + 0·30 sin 9000t] cos (6 × 10⁶t) volt
What are the sidebands of the signals in radians?

1. 5 × 10³ and 9 × 10³
2. 5·91 × 10⁶ , 5·995 × 10⁶ , 6·005 × 10⁶ and 6·009 × 10⁶
3. 4 × 10³ , 1·4 × 10⁴
4. 1 × 10⁶ , 1·1 × 107, 3 × 10⁶ , 1·5 × 10⁷

Correct Option: B

The given equation. e(t) = 50[1 + 0·89 cos 5000 t + 0·30 sin 9000t] cos (6 × 10⁶t) volt
Let 5000 = ω_m1 or ω_m1 = 0·005 MHz
9000 = ω_m2 or ω_m2 = 0·009 MHz
6 × 106 = ω_c1 or ω_c1 = 6 MHz
e(t) = 50[cos ω_c1 t + 0·89 cos ω_m1t. cos ω_c1t + 0·30 sin ω_m2t]
Sidebands of the signals are at
ω_c1 ± ω_m1 and ω_c1 ± ω_m2, frequency
i.e. (6 ± 0·005) MHz and (6 ± 0·009) MHz
6·005 × 10⁶, 5·995 × 10⁶, 6·009 × 10⁶, 5·991 × 10⁶
Hence alternative (B) is the correct choice.