Question

A line has a signal-to-noise ratio of 2000 and a bandwidth of 5000khz. what is the maximum data rate supported by this line?

Answer 1

it can be 4000 khz or 3900 khz

Answer 2

Concept

A signal/noise over $0dB$ indicates that the amplitude is larger than the amplitude. the upper the ratio, the higher the signal quality.

Given

We are only if there's a signal/noise of $2000$ and bandwidth $5000khz$ of a line.

Find

We have to search out the utmost rate supported by line.

Solution

We will use the formula $N_{max}=B\log_{2}(1+SNR)$.

Here, bandwidth, $B=5000\times 10^3hz$ and signal-to-noise ratio, $SNR=2000$.

Substitute these values within the formula.

$\begin{aligned}N_{max}&=5000\times10^{3}\times \log_{2}(1+2000)\\ &=5000\times 10^{3}\times \log_{2}(2001)\\ &=5000\times 10^{3}\times 10.96\\ &=54.8Mbps\end{aligned}$

Hence, the most data rate supported by $54.8Mbps$ the line.

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