Find the maximum achievable data rate

Question

The signal to noise ratio for a voice grade line is 30.1 dB (decibels) or a power ratio of 1023: 1.

The maximum achievable data rate on this line whose spectrum ranges from 300 Hz to 4300 Hz is

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(a) 6200 bps

(b) 9600 bps

(c) 34000 bps

(d) 31000 bps.

Answer 1

Max data rate is given by famous Shannon Hartley Theorem.

$C = B*\log \left ( 1+\frac{S}{N} \right )$
B = (4300-300) = 4000 Hz

C = 4000 * log₂ (1+1023) = 4000 x 10 = 40000 bps.

None of the option is correct.