C.5. Doppler Effect (HL Additional Content)

When there is relative motion between a sound source and an observer:

● Source Approaching Observer:
○ Observed Frequency: Increases
○ Equation:
$f' = f \left( \frac{v + v_o}{v - v_s} \right)$

● Source Receding from Observer:
○ Observed Frequency: Decreases
○ Equation:
$f' = f \left( \frac{v - v_o}{v + v_s} \right)$

Where:
● $f'$ is the observed frequency
● $f$ is the source frequency
● $v$ is the speed of sound in the medium
● $v_o$ is the speed of the observer
● $v_s$ is the speed of the source

The Doppler Effect for sound explains how the frequency of sound waves changes due to the movement of the source or observer. When the source of the sound is moving towards the observer, it compresses the sound waves, leading to a higher frequency or pitch. This is known as an increase in observed frequency. Conversely, if the source is moving away from the observer, the sound waves are stretched out, resulting in a lower frequency. The equations provided describe how to calculate the observed frequency based on the original frequency and the speeds of the source and observer.

Imagine standing on the side of the road as an ambulance with its siren on approaches you. As it moves towards you, the sound of the siren seems to get higher in pitch. When it passes by and moves away, the sound lowers in pitch. This change in sound due to the movement of the ambulance is a practical demonstration of the Doppler Effect.

In the context of light, the Doppler Effect results in a shift in the observed wavelength:

● Approaching Source: Blue Shift (shorter wavelength)
● Receding Source: Red Shift (longer wavelength)

Equation:
$\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$
Where:
● $\Delta \lambda$ is the change in wavelength
● $\lambda$ is the original wavelength
● $v$ is the relative velocity between source and observer
● $c$ is the speed of light

The Doppler Effect also applies to light waves. When a light source moves towards an observer, the observed wavelength of the light decreases, resulting in a blue shift. This is because the waves get compressed. If the light source is moving away from the observer, the wavelength increases, resulting in a red shift as the waves are stretched out. The equation provided indicates how to calculate the change in wavelength based on the relative velocity between the source and observer, with respect to the speed of light.

When astronomers observe stars or galaxies, they often see blue shifts or red shifts in the light they emit. If a galaxy is moving towards us, its light is blue-shifted, indicating that it is speeding in our direction. If it's moving away, the light is red-shifted. This effect allows scientists to understand the movement of celestial bodies in the universe.

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