Speed cameras make use of the Doppler effect - Leaving Cert Physics - Question c - 2020

The Doppler effect can be illustrated using a diagram where the source of sound emits waves in a non-concentric circle pattern. As the source moves towards a stationary observer, the waves are compressed, resulting in a higher frequency and shorter wavelength reaching the observer. Conversely, if the source were moving away, the waves would be stretched, leading to a lower frequency and longer wavelength.

Given that the observed frequency is 20% greater than the original frequency, we can express this mathematically. Let the original frequency be $f$; the observed frequency $f' = 1.2f$. Using the Doppler effect formula:

$f' = f \frac{v}{v - u}$

where $v$ is the speed of sound in air (340 m/s) and $u$ is the speed of the source. Rearranging gives:

$u = v \left(1 - \frac{f}{f'}\right)$

Substituting $f' = 1.2f$, we get:

$u = 340 \left(1 - \frac{f}{1.2f}\right) = 340 \left(1 - \frac{1}{1.2}\right) = 340 \left(\frac{0.2}{1.2}\right) = 56.7 \, \text{m/s}$

The red-shift observed in galaxies indicates that they are moving away from us, implying that the universe is expanding. This observation supports the Big Bang theory and helps us understand the dynamics of cosmic expansion.