---
title: "Doppler effect; cordless phone path loss"
subject: "Wireless Communication"
chapter: 3
key: "semester_7/wireless_communication:doppler-effect-cordless-phone"
source: https://www.bctengineer.com/q/semester_7/wireless_communication/doppler-effect-cordless-phone
site: BCT Engineering
---

# Doppler effect; cordless phone path loss

Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks

- Asked in: 2080 Chaitra, 2+4 marks
- Video: [Doppler Shift - Mobile Radio Propagation - Mobile Communication System](https://www.youtube.com/watch?v=nfk_9B3ZDFk) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/wireless_communication/doppler-effect-cordless-phone
- Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3

## Question

Define Doppler's effect in small scale fading. (i) Given a cordless phone operating at 52000 kHz frequency which has a range of 50 m. Determine the free space path loss.

## Short answer

Doppler effect is the change in received frequency due to relative motion, with maximum shift fm = v/λ. For the cordless phone at 52 MHz and 50 m, free space path loss is 40.7 dB.

## Answer

#### Doppler effect in small-scale fading
The **Doppler effect** is the apparent change in the frequency of a received signal due to relative motion between transmitter and receiver. A mobile moving at speed *v* receives a wave arriving at angle θ to its direction of motion with a frequency shift

```text
fd = (v/λ)·cosθ
```
In a multipath channel, waves arrive from many angles, so each has a different Doppler shift. The received spectrum spreads over fc ± fm (fm = v/λ). This **Doppler spread** causes random frequency modulation and makes the channel time-varying; it decides whether fading is fast or slow (through coherence time Tc ≈ 0.423/fm).

#### Free space path loss of the cordless phone
Given: f = 52 000 kHz = 52 MHz, d = 50 m. Assuming unity gain antennas:

```text
λ = c/f = 3×10⁸ / 52×10⁶ = 5.769 m

PL = 20 log(4πd/λ)
   = 20 log(4π × 50 / 5.769)
   = 20 log(108.91)
   = 40.74 dB
(check: 32.44 + 20 log 52 + 20 log 0.05
       = 32.44 + 34.32 − 26.02 = 40.74 dB)
```

**Answer: Free space path loss ≈ 40.7 dB.**

## Check yourself

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

1. A mobile moving at speed v receives a wave at angle θ to its motion. The Doppler shift is:
   A. fd = (v/λ) sinθ
   B. fd = (λ/v) cosθ
   C. fd = (v/λ) cosθ
   D. fd = v λ cosθ
   Answer: C. fd = (v/λ)cosθ, with maximum fm = v/λ. (Key point: Doppler shift formula)

2. What does Doppler spread cause in a multipath channel?
   A. Spectral spreading over fc ± fm and a time-varying channel
   B. A constant channel
   C. Reduction of path loss exponent
   D. Only a fixed frequency offset
   Answer: A. Waves from many angles have different shifts, spreading the spectrum and deciding fast or slow fading via Tc. (Key point: Doppler spread effect)

3. For the 52 MHz phone at 50 m with unity-gain antennas, the free-space path loss is about:
   A. 20.7 dB
   B. 60.7 dB
   C. 80.7 dB
   D. 40.7 dB
   Answer: D. λ = 5.769 m, so PL = 20 log(4π x 50/5.769) = 20 log 108.91 = 40.74 dB. (Key point: Free-space loss method)

## Close variants set in other exams

- [Numerical: cordless phone free space path loss](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Acordless-phone-path-loss) — Wireless Communication, chapter 3, asked 2×

## Related in Wireless Communication

- [Large scale path loss and small scale fading](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Alarge-scale-loss-small-fading) — Wireless Communication, chapter 3
- [Numerical: two-ray vs free-space path loss at 800 MHz](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Atwo-ray-path-loss-800mhz) — Wireless Communication, chapter 3
- [Small scale fading types and factors](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Asmall-scale-fading-types-factors) — Wireless Communication, chapter 3, asked 2×
- [Small scale fading and influencing factors](https://www.bctengineer.com/question.md?key=semester_7%2Fwireless_communication%3Asmall-scale-fading-factors) — Wireless Communication, chapter 3

## Related in other subjects

- [Free space path loss: 6 GHz, 10,500 km](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afspl-derivation-6ghz-10500km) — Propagation and Antenna, chapter 5
- [Friis equation and free space path loss](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afriis-path-loss-free-space) — Propagation and Antenna, chapter 5, asked 2×