Doppler Effect Receding Source Calculator

What is the Doppler Effect for a Receding Source?

The Doppler effect for a receding source is a phenomenon in which the observed frequency of a wave decreases as the source moves away from the observer. This effect is named after Austrian physicist Christian Doppler, who described it in 1842. In the case of a receding source, the wavelengths are stretched out, resulting in a lower perceived frequency.

Formula

The formula for the Doppler effect with a receding source is:

\[ f' = f \cdot \frac{c}{c + v} \]

Where:

• \( f' \) is the observed frequency (in Hz)
• \( f \) is the original frequency emitted by the source (in Hz)
• \( c \) is the speed of sound in the medium (in m/s)
• \( v \) is the speed of the source receding from the observer (in m/s)

Calculation Steps

Let's calculate the observed frequency for a receding source:

1. Given:
   • Original frequency (\( f \)) = 440 Hz
   • Speed of sound (\( c \)) = 343 m/s
   • Source speed (\( v \)) = 20 m/s
2. Apply the Doppler effect formula: \[ f' = f \cdot \frac{c}{c + v} \]
3. Substitute the known values: \[ f' = 440 \text{ Hz} \cdot \frac{343 \text{ m/s}}{343 \text{ m/s} + 20 \text{ m/s}} \]
4. Perform the calculation: \[ f' = 440 \text{ Hz} \cdot \frac{343 \text{ m/s}}{363 \text{ m/s}} \approx 415.43 \text{ Hz} \]

Example and Visual Representation

Let's visualize the Doppler effect for a receding source:

This diagram illustrates:

• The sound source (blue circle) moving away from the observer (red dot)
• The sound waves (green curves) stretched out behind the moving source
• The observer perceiving a lower frequency due to the stretched waves