What happens to the observed frequency of light when source and observer approach each other?

What happens to the observed wavelength of light from a receding source?

State the longitudinal relativistic Doppler formula for an approaching source.

State the longitudinal relativistic Doppler formula for a receding source.

A source emits \(5.00\times10^{14}\,\mathrm{Hz}\) and approaches slowly enough that the observed frequency is \(6.00\times10^{14}\,\mathrm{Hz}\). Is this a redshift or blueshift?

A spectral line has rest wavelength \(500\,\mathrm{nm}\) and observed wavelength \(550\,\mathrm{nm}\). Find the redshift \(z\).

A source emitting \(5.00\times10^{14}\,\mathrm{Hz}\) approaches at \(0.200c\). Find the observed frequency.

A source emitting \(6.00\times10^{14}\,\mathrm{Hz}\) recedes at \(0.200c\). Find the observed frequency.

A rest wavelength \(500\,\mathrm{nm}\) is observed at \(650\,\mathrm{nm}\). Find \(z\) and state whether the source is approaching or receding.

A source recedes at \(0.600c\). By what factor is the observed frequency changed?

A source approaches at \(0.600c\). By what factor is the observed wavelength changed?

A galaxy has redshift \(z=0.500\). What is the ratio \(\lambda_o/\lambda_s\)?

For a receding source, derive \(\lambda_o/\lambda_s=\sqrt{(1+\beta)/(1-\beta)}\).

A source has observed wavelength twice its rest wavelength. Find the recession speed.

A source emits at \(400\,\mathrm{nm}\) and approaches at \(0.800c\). Find the observed wavelength.

Derive the source speed in terms of the wavelength ratio \(R=\lambda_o/\lambda_s\) for a receding source.

Why is the relativistic Doppler effect for light symmetric between source motion and observer motion?

Show that the approaching and receding Doppler factors are reciprocals.

Explain why using the sound Doppler formula for light in vacuum is conceptually wrong.

Show that the receding relativistic Doppler formula becomes the approximate low-speed redshift \(z\approx\beta\).