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