A) Show that the surface temperature of a star can be inferred from measurements of blackbodyfluxes at two different frequencies, even if the stellar radius and distance are unknown. b) Explain why in practice this method does not work well if both frequencies are on theRayleigh-Jeans side of the spectrum, hνkT.
c) Derive a simple, approximate expression for the temperature when both measurements areon the Wien tail, hνkT.
d) Derive an expression for the star’s radius if a distance measurement is also available (e. g.,from parallax).

The answers to the questions have been solved in the attachment.

Explanation:

The answers to part a to e are all contained in the attachment. For answer part b, temperature and frequency were assumed to be fixed or constant. V² is directly proportional to T telling us that variation in T gives us a square in the frequency variation. This tells us why it is difficult when both frequencies are on this side of the black body.

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.