Doppler Source Without Frequency

Mahi Tuatahi

Rearrange \(f' = f\frac{v_{w}}{v_{w} \pm v_{s}}\) for \(v_{s}\) when:

1. Source is approaching the observer
2. Source is retreating from the observer

Show me your homework!

Doppler Skill 4: Calculating \(v_{s}\) Without \(f\)

1. Rearrange \(f' = f\frac{v_{w}}{v_{w} \pm v_{s}}\) to make \(f\) the subject.
2. Write two equations, one with \(f_{approaching}\) and one with \(f_{receeding}\) in place of \(f'\).
3. Because \(f\) is constant, you can now make these two equations equal to each other.
4. Substitute your knowns.
5. Solve for \(v_{s}\)!

NB: Unfortunately, \(f\) is not the midpoint between \(f_{a}\) and \(f_{r}\) for the same reason that the average of 1/4 and 1/6 is not 1/5.

To solve, rearrange the dopper formula to make \(f\) the subject and then set \(f_{approaching} = f_{receeding}\).

We can do this because the frequency of the source is constant (at least in Y12/13 Physics).

\[ \begin{aligned} f' &= f\frac{v_{w}}{v_{w} \pm v_{s}} \newline f &= f' \frac{v_{w} \pm v_{s}}{v_{w}} \newline\newline f_{approaching} &= f_{receeding} \newline f_{a} \frac{v_{w} - v_{s}}{v_{w}} &= f_{r} \frac{v_{w} + v_{s}}{v_{w}} \newline \text{substitute and solve...} \end{aligned} \]

Practice: Calcuating \(v_{s}\) without \(f\):

1. HWB Q9c
2. Textbook Activity 6A Q3
3. P3.3 Worksheet #4 Q3a