What is the modulation index for an FM phone signal with a maximum frequency deviation of 3,000 Hz and a modulating frequency of 1,000 Hz?

To determine the modulation index for a frequency modulated (FM) signal, you can use the formula for the modulation index, which is defined as the ratio of the frequency deviation to the modulating frequency. In this case, the maximum frequency deviation is 3,000 Hz and the modulating frequency is 1,000 Hz.

The modulation index (β) can be calculated as:

[

\text{Modulation Index} (β) = \frac{\text{Maximum Frequency Deviation}}{\text{Modulating Frequency}}

]

Substituting the given values:

[

β = \frac{3000, \text{Hz}}{1000, \text{Hz}} = 3

]

This calculation shows that the modulation index is 3, indicating that the frequency deviation is three times the modulating frequency.

The modulation index is essential in FM transmission as it affects the bandwidth and the amount of frequency deviation utilized in the modulation process, which directly impacts audio quality and coverage. Thus, for an FM phone signal with the provided parameters, the correct modulation index value is 3.