IB Physics SL C.5.3 Light Doppler Approximation

Practise applying the low-speed light Doppler approximation to fractional frequency or wavelength shifts, assigning redshift and blueshift signs and calculating radial velocity.

Exam points

use |Δf|/f ≈ |Δλ|/λ ≈ v/c only when relative speed is small compared with c
assign longer wavelength and lower frequency to recession, and the reverse to approach
calculate radial speed from a spectral shift using rest and observed values in matching units

[Maximum number: 2]

Star A is a main sequence star.

The data for Star A and the Sun are given in a table.

Table for Question C.5.3—Light Doppler approximation question 1 — IB Physics SL

Determine the speed, in $\mathrm{km} \mathrm{s}^{-1}$ , of Star A relative to Earth.

$\begin{aligned} v=\frac{\Delta \lambda}{\lambda} c=\frac{0.007}{100} \times 3 \times 10^{8}=21000 21 \mathrm{~km} \mathrm{~s}^{-1} \end{aligned}$

Allow ECF for MP2.

Do not award MP1 for use of the Doppler formulas for sound and mechanical waves.

[2]

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C.5.3—Light Doppler approximation question 1