Question

For speech signals, frequency range $300\,Hz$ to $3100\,Hz$ is considered adequate. Therefore, what is its bandwidth?
(A) $2800$
(B) $2700$
(C) $3400$
(D) $2900$

Answer 1

A key characteristic of the bandwidth is any band width can carry the same amount of information, where that the band is located in the frequency spectrum. Bandwidth is the difference of the upper and the lower frequencies in a continuous band of frequencies. By using this the bandwidth is determined for the given frequencies.

Useful formula:
The bandwidth of the two given frequencies is given by,
$B = {F_H} - {F_L}$
Where, $B$ is the band width in any frequency range, ${F_H}$ is the highest frequency of the band and ${F_L}$ is the lowest frequency of the band.

Complete step by step solution:
Given that,
The frequency range is between $300\,Hz$ to $3100\,Hz$.
The highest frequency of the band is, ${F_H} = 3100\,Hz$.
The lowest frequency of the band is, ${F_L} = 300\,Hz$.
Now,
The bandwidth of the two given frequencies is given by,
$B = {F_H} - {F_L}\,.....................\left( 1 \right)$
By substituting the highest frequency of the band and the lowest frequency of the band in the above equation (1), then the above equation (1) is written as,
$B = 3100 - 300$
On subtracting the above equation, then the above equation is written as,
$B = 2800\,Hz$
Thus, the above equation shows the band width of the given frequency range.

Hence, the option (A) is the correct answer.

Note: Both frequency and bandwidth are the two major terms related to the data transmission. The major difference between the frequency and the bandwidth is that the frequency shows the number of complete cycles appearing in the unit time. As against bandwidth is the overall amount of data transmitted in a unit time.