Doppler Effect

Overview

Engineering reference data for Doppler Effect in acoustics.

Key Formulas

Speed of Sound

$c = \sqrt{\gamma R T}$

Speed of sound in an ideal gas.

Sound Level

$L = 10 \log_{10}(I/I_0)$

Decibel level.

Wavelength

$\lambda = c / f$

Wavelength = speed / frequency.

Variables

Practical Example

Scenario: A train traveling at 200 km/h (55.6 m/s) passes a stationary bell emitting a sound at 1000 Hz. The air temperature is 20°C, making the speed of sound (c) 343 m/s.

The observed frequency (f_r) for a passenger on the train is calculated using the Doppler formula: $f_r = f_s \left( \frac{c + v_r}{c + v_s} \right)$

1. Approaching the Bell: The passenger (receiver) is moving towards the stationary source (v_s = 0 m/s). $f_{r, \text{approach}} = (1000 \text{ Hz}) \left( \frac{343 \text{ m/s} + 55.6 \text{ m/s}}{343 \text{ m/s} + 0 \text{ m/s}} \right) = 1162 \text{ Hz}$

2. Moving Away from the Bell: After passing, the passenger (receiver) is moving away from the source (v_r becomes -55.6 m/s). $f_{r, \text{recede}} = (1000 \text{ Hz}) \left( \frac{343 \text{ m/s} - 55.6 \text{ m/s}}{343 \text{ m/s} + 0 \text{ m/s}} \right) = 838 \text{ Hz}$

This demonstrates the characteristic increase in pitch as the source approaches and the decrease in pitch as it moves away.

Interactive Charts

References

• Original Source