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The Doppler effect describes the change in frequency and wavelength of waves, such as sound or light, due to the relative motion of the source and observer. It's observed as a pitch change in sound or a redshift/blueshift in light. The classical and relativistic Doppler formulas are essential for understanding phenomena from passing sirens to the expanding universe, a concept confirmed by Edwin Hubble's redshift observations of distant galaxies.

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## Definition and Explanation of the Doppler Effect

### Physical Phenomenon

The Doppler effect is a change in the frequency and wavelength of waves perceived by an observer due to relative motion between the source and observer

### Classical Doppler Effect Formula

Formula Components

The classical Doppler effect formula takes into account the observed frequency, speed of the wave, velocity of the observer and source, and actual frequency of the source

Application in Everyday Situations

The classical Doppler effect formula is used to understand and predict the change in frequency of waves, such as the siren of a passing emergency vehicle

### Relativistic Doppler Effect Formula

Formula Components

The relativistic Doppler effect formula takes into account time dilation, length contraction, observed frequency, emitted frequency, relative velocity, and the speed of light

Application in High-Velocity Contexts

The relativistic Doppler effect formula is crucial for accurate measurements in high-velocity contexts, such as in astrophysics and cosmology

## Influence of the Doppler Effect on Light from Moving Sources

### Redshift and Blueshift

The Doppler effect causes light from a moving source to appear redshifted or blueshifted, depending on the direction of motion

### Importance in Astronomy

Measurement of Velocities

The Doppler effect is a vital tool in astronomy for measuring the velocities of celestial objects relative to the Earth

Understanding the Dynamics of the Universe

The Doppler effect helps in understanding the dynamics of the universe, such as the expansion of the universe

## Edwin Hubble's Discovery of the Expanding Universe

### Redshift of Light from Distant Galaxies

Edwin Hubble's observations of the redshift of light from distant galaxies were instrumental in the discovery of the expanding universe

### Proportional Relationship between Redshift and Distance

Hubble's discovery of the proportional relationship between redshift and distance led to the understanding that the universe is expanding at an increasing rate

### Significance in Cosmology

Hubble's discovery of the expanding universe has become a cornerstone of modern cosmology and our understanding of the universe's evolution