Worked example: An FM station has maximum frequency deviation Δf = 75 kHz and the highest audio frequency fm = 15 kHz. Find the modulation index and the approximate bandwidth. Step 1: Modulation index β = Δf / fm = 75 kHz / 15 kHz = 5. Step 2: Carson's rule for bandwidth: BW ≈ 2(Δf + fm) = 2(75 + 15) kHz = 180 kHz. Step 3: Compare with AM for the same audio: AM bandwidth = 2·fm = 30 kHz. Conclusion: this FM station occupies about 180 kHz — six times the AM bandwidth — which is why FM gives much better sound quality but fewer stations fit in the band. (Real FM channels are rounded to 200 kHz spacing.)