Describe the Doppler effect.

A spectral line from a source on Earth has a frequency of 4.672×10¹⁴ Hz. When this same line is observed from a distant galaxy it is found to have shifted to 4.669×10¹⁴ Hz.

(i) State the direction of the motion of the galaxy relative to Earth.

(ii) Deduce the speed of the galaxy relative to Earth.

(apparent) shift in frequency of wave;
when relative motion between source of waves and observer;
approach gives increase in frequency / recession decrease in frequency;
Allow answer in terms of red or blue shifts.

(i) galaxy moving away from Earth;

(ii) rearranges data book equation thus \(v \approx \frac{{\Delta f}}{f}c\);
\(v = \frac{{3.0 \times {{10}^{11}} \times 3 \times {{10}^8}}}{{4.672 \times {{10}^{14}}}}\);
\(v = 1.93 \times {10^5}{\rm{m}}{{\rm{s}}^{ - 1}}\);