The Doppler effect is a change in the observed frequency of a wave when there is relative motion between the source of the wave and the observer. For an approaching source, the observed frequency is higher than the emitted frequency. This phenomenon is named after Austrian physicist Christian Doppler, who described it in 1842.

The formula for the Doppler effect with an approaching 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 approaching the observer (in m/s)

Let's calculate the observed frequency for an approaching source:

- Given:
- Original frequency (\( f \)) = 440 Hz
- Speed of sound (\( c \)) = 343 m/s
- Source speed (\( v \)) = 20 m/s

- Apply the Doppler effect formula: \[ f' = f \cdot \frac{c}{c - v} \]
- Substitute the known values: \[ f' = 440 \text{ Hz} \cdot \frac{343 \text{ m/s}}{343 \text{ m/s} - 20 \text{ m/s}} \]
- Perform the calculation: \[ f' = 440 \text{ Hz} \cdot \frac{343 \text{ m/s}}{323 \text{ m/s}} \approx 467.18 \text{ Hz} \]

Let's visualize the Doppler effect for an approaching source:

This diagram illustrates:

- The sound source (blue circle) moving towards the observer (red dot)
- The sound waves (green curves) compressed in front of the moving source
- The observer perceiving a higher frequency due to the compressed waves

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