What is the deviation ratio of an FM phone signal having a maximum frequency swing of plus or minus 5 kHz if the highest modulation frequency is 3 kHz?

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Deviation ratio takes the maximum permitted frequency swing over the highest audio frequency the system passes: 5 kHz ÷ 3 kHz ≈ 1.67. It is the worst-case value of the modulation index, so it is fixed by the design limits of the system rather than by the audio present at any moment.