According to Carson’s rule, Bandwidth B and modulating frequency fm are related as*2 pointsB = 2(Δf + fm) HzB = fm HzB < 2fm HzB > 2fm Hz

To answer your question about Carson’s rule and how the bandwidth (B) relates to the modulating frequency (fm), let's explore the given options.

Understanding Carson's Rule

Carson's rule provides a method to calculate the bandwidth required for frequency modulation. The rule states that the total bandwidth (B) for frequency modulation can be calculated by considering the frequency deviation (Δf) and the modulating frequency (fm). The formula is given by:

$B = 2(\Delta f + f_m)$

This means that the bandwidth is double the sum of the frequency deviation and the modulating frequency.

Analyzing the Options

1. B = 2(Δf + fm) Hz - This option correctly represents Carson’s rule as stated above.
2. B = fm Hz - This is not correct according to Carson’s rule as it doesn't consider the frequency deviation.
3. B < 2fm Hz - This may not hold true in general cases since B can be greater than or equal to 2fm depending on Δf.
4. B > 2fm Hz - Like the previous point, this is not necessarily true as B depends on the values of Δf and fm.

Final Answer

The correct relationship according to Carson's rule is B = 2(Δf + fm) Hz.