---
title: "Single tone FM parameters"
subject: "Data Communication"
chapter: 5
key: "semester_5/data_communication:fm-single-tone-numeric"
source: https://www.bctengineer.com/q/semester_5/data_communication/fm-single-tone-numeric
site: BCT Engineering
---

# Single tone FM parameters

Data Communication · Chapter 5: Data Encoding and Modulation

- Asked in: 2074 Chaitra, 8 marks
- Video: [Carson's Rule in Frequency Modulation - Calculating Bandwidth of FM - Solved Problems on Carson Rule](https://www.youtube.com/watch?v=dj5emtMrMY0) — Engineering Made Easy
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/fm-single-tone-numeric
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-5

## Question

A single tone FM is represented by the voltage equation as v(t) = 12cos(6×10⁸t + 5sin1250t). Determine the following: a) Carrier frequency b) Modulating frequency c) Modulation index d) Maximum frequency deviation

## Short answer

Carrier frequency fc=ωc/2π=6×10⁸/(2π)≈95.5 MHz. Modulating frequency fm=1250/(2π)≈199 Hz. Modulation index β=5. Maximum deviation Δf=β fm≈995 Hz.

## Answer

v(t) = 12 cos(6×10⁸t + 5 sin 1250t)

Compare with the standard FM equation v(t) = Ac cos(ωct + β sin ωmt):
- ωc = 6×10⁸ rad/s
- ωm = 1250 rad/s
- β = 5
- Ac = 12 V

#### a) Carrier frequency
fc = ωc/2π = 6×10⁸ / 6.283 = **95.5 MHz**

#### b) Modulating frequency
fm = ωm/2π = 1250 / 6.283 = **198.9 Hz** (about 199 Hz)

#### c) Modulation index
β = **5**

#### d) Maximum frequency deviation
Δf = β × fm = 5 × 198.9 = **994.7 Hz** (about 995 Hz)

(Bandwidth by Carson's rule = 2(Δf + fm) = 2(994.7 + 198.9) = 2.39 kHz.)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. fc = ωc/2π:
   A. 95.5 MHz
   B. 600 MHz
   C. 6×10⁸ Hz exactly
   D. 9.55 MHz
   Answer: A. 6e8/6.283. (Key point: Carrier)

2. fm:
   A. 1250 Hz
   B. 198.9 Hz
   C. 5 Hz
   D. 1989 Hz
   Answer: B. 1250/2π. (Key point: fm)

3. β in v(t):
   A. 1250
   B. 12
   C. 5
   D. 0.2
   Answer: C. Coefficient of sin. (Key point: Index)

4. Δf = β fm:
   A. About 199 Hz
   B. About 6 kHz
   C. About 5 Hz
   D. About 995 Hz
   Answer: D. 5 x 198.9. (Key point: Deviation)

## Related in Data Communication

- [Frequency modulation](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afm-explain) — Data Communication, chapter 5
- [AM numerical: 10 sin1000πt on 50 sin 2π×10⁵t](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aam-numeric-10sin1000pi) — Data Communication, chapter 5
- [AM numerical: 20 sin2π500t on 60 sin2π10⁶t](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aam-numeric-20sin500) — Data Communication, chapter 5
- [AM versus FM](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aam-vs-fm-compare) — Data Communication, chapter 5, asked 2×
- [AM numerical: 10 sin1000πt on 50 sin200000πt](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aam-numeric-10sin1000pi-800) — Data Communication, chapter 5

## Related in other subjects

- [Angle modulation; single tone FM time and frequency domain](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aangle-mod-single-tone-fm-time-freq) — Communication Systems, chapter 3
- [FM numerical: 10 kHz baseband, 100 MHz carrier, 75 kHz deviation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-10khz-100mhz-75khz) — Communication Systems, chapter 3
- [DSB-FC single tone expression and modulation index](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adsbfc-single-tone-index) — Communication Systems, chapter 2
- [FM numerical: 102.4 MHz carrier, 75 kHz deviation](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Afm-102-4mhz-75khz) — Communication Systems, chapter 3