Doppler effect (A-level only) Flashcards – AQA A-level Physics (7408)

For electromagnetic radiation, what is the low-speed Doppler formula for the fractional frequency shift? Take $v$ as positive towards the observer, $f$ as the emitted frequency, and $\Delta f$ as observed minus emitted frequency.

$\frac{\Delta f}{f}=\frac{v}{c}$

For electromagnetic radiation, what is the low-speed Doppler formula for redshift $z$? Take $v$ as positive towards the observer, $\lambda$ as the emitted wavelength, and $\Delta\lambda$ as observed minus emitted wavelength.

$z=\frac{\Delta\lambda}{\lambda}=-\frac{v}{c}$

How do approach and recession affect the observed frequency and wavelength of electromagnetic radiation?

• Approach: higher frequency, shorter wavelength.
• Recession: lower frequency, longer wavelength.

How can spectral features be used to determine a galaxy’s or quasar’s redshift?

Compare their observed wavelengths with their rest wavelengths.

When can $z=-v/c$ be used to estimate radial velocity from redshift?

Only when the relevant speed is much smaller than the speed of light. It must not be treated as exact at large redshifts.

Why do a binary star's spectral lines shift as it orbits, when the system is viewed edge-on?

The star's line-of-sight velocity changes as it moves towards and away from the observer.

How can a star's line-of-sight velocity be determined from a measured fractional spectral shift?

Apply the low-speed Doppler relationship to the fractional frequency or wavelength shift.

For a circular binary orbit viewed edge-on, how is a star's orbital speed related to its maximum line-of-sight velocity?

It equals the maximum magnitude of the line-of-sight orbital velocity, after allowing for the system's motion along the line of sight.

How do the two stars in a binary system move about their common centre of mass?

They move in opposite directions.

How do the orbital periods of the two stars in a binary system compare?

They have the same orbital period.

For a circular orbit, how is orbital radius $r$ calculated from orbital speed $v$ and period $T$?

$r = \frac{vT}{2\pi}$

What relation connects the masses and orbital speeds of two stars in a binary system?

$m_1v_1 = m_2v_2$