The Expanding Universe Additional reading: Higher Physics for CfE, p Notes p.42 Watch or listen to the following video clips: Doppler Effect

The Expanding Universe Notes p.42 Objects Moving Towards Us We are all familiar with the “nee naw” sound from approaching emergency vehicles. As the vehicle approaches, the sound we hear is higher in pitch than when the vehicle is stationary. This is because, as the sound source moves towards us, the sound wavelength it emits gets “squashed”. This shortening of wavelength is detected as a sound with higher frequency (or “pitch”). 1. Doppler Effect

The sound waves are distorted like this… stationary source moving source stationary observer The change in the “observed” frequency is what we call “The Doppler Effect”. The Doppler Effect is observed with sound and light, as well as with other waves.

Blue Shift We can observe the Doppler Effect in galaxies. Obviously we don’t hear light, but we can detect a change in their spectral lines (showing the e.m. wavelengths emitted). If the galaxy is moving towards our Milky Way, the spectra is shifted towards higher frequencies and shorter wavelengths. We call this a “Blue Shift”. This is currently the case with our neighbouring galaxy, Andromeda. No need to worry – it’s 2.5 million light years away!

Objects Moving Away From Us As an emergency vehicle moves away from us, the sound we hear is lower in pitch than for the stationary vehicle. This is because, as the sound source moves away from us, the sound wavelength it emits gets “stretched”. This lengthening of wavelength is detected as a sound with lower frequency (or “pitch”).

Red Shift As stars and galaxies move away from us (that’s most of them!) we detect a change in their spectral lines towards lower frequencies and longer wavelengths. We call it a “Red Shift”. Light from most galaxies and stars is “red shifted”, so scientists believe that the Universe is expanding. This is strong evidence for The Big Bang Theory, coming up in this course very soon! Note … localised gravity can explain the blue shift for Andromeda.

Red Shift and Blue Shift Images 1.Colour your notes to emphasise the shifts. 2.What can you say about Galaxies A, B and C below?

For a sound or light source moving towards a stationary observer: f o = f s Doppler Effect Calculations v (v – v s ) For a sound or light source moving away from a stationary observer: f o = f s v (v + v s ) f s = source frequency in Hz f o = observed frequency in Hz v = velocity of the sound or light in ms -1 v s = velocity of the source in ms -1

IMPORTANT NOTE These Doppler Effect equations cannot be used for very fast moving sources because relativistic effects would be substantial. By “very fast” or “relativistic speeds” we generally mean speeds over 10% of the speed of light or over 3 x 10 7 ms -1 or over 0.1c. The Higher course doesn’t cover these calculations … BIG PHEW!!!

Worked Examples f o = ? f s = 1000 Hz v = 340 ms -1 v s = 20 ms -1 Worked Example 1 A police car siren emits sound with a frequency of 1000 Hz. The speed of sound in air is 340 ms -1. a) Determine the frequency observed by a stationary pedestrian if the police car is moving towards the pedestrian at 20 ms -1. v (v - v s ) f o = f s 340 ( ) = 1000 = 1063 Hz 4 sig figs is 1 too many…1060 Hz is acceptable.

Worked Examples v = 340 ms -1 f o = 1063 Hz o = ? Worked Example 1 A police car siren emits sound with a frequency of 1000 Hz. The speed of sound in air is 340 ms -1. b) Determine the corresponding wavelength of sound detected by the observer. v fofo o = = = 0.32 m

Worked Examples Worked Example 2 A 410 nm spectral line from Hydrogen is examined in a laboratory on Earth. A stellar spectrum shows this line as red shifted to 440 nm a) Calculate the frequency of the spectral line from the Hydrogen source examined in the laboratory. v = 3 x 10 8 ms -1 f s = ? s = 410 x m v f s = s 3 x x = = 7.32 x Hz

Worked Examples Worked Example 2 A 410 nm spectral line from Hydrogen is examined in a laboratory on Earth. A stellar spectrum shows this line as red shifted to 440 nm b) Calculate the frequency of the spectral line recorded in the stellar spectrum. v = 3 x 10 8 ms -1 f o = ? o = 440 x m v f o = o 3 x x = = 6.82 x Hz

Worked Examples Worked Example 2 A 410 nm spectral line from Hydrogen is examined in a laboratory on Earth. A stellar spectrum shows this line as red shifted to 440 nm c) Without relativistic considerations, determine the velocity of the star. f o = 6.82 x Hz f s = 7.32 x Hz v = 3 x 10 8 ms -1 v s = ? v (v + v s ) f o = f s 3 x 10 8 (3 x v s ) 6.82 x = 7.32 x = 2.2 x 10 7 ms x (3 x v s ) = 6.82 x x x 10 8 v s =

“Redshift” Quantified Edwin Hubble noticed, way back in the 1920s, that light from the stars and galaxies he observed was red shifted. So he presumed all stars and galaxies were moving apart. He quantified the redshift (z) as “the ratio of the change in wavelength to the wavelength with the source at rest”. In short …z = o - rest rest

Of course later it was discovered that some stars and 1 galaxy are actually moving towards us. In this case the redshift value, z, is negative. So a negative “redshift” is, in fact, a blue shift. For non-relativistic speeds (that’s less than about 10% of the speed of light, or 0.1c), the redshift of a star or galaxy can be simplified to z = v c

Worked Example 3 Consider again the Hydrogen line fromWorked Example nm recorded in the lab and 440nm observed from a star. a)Calculate the redshift value, z. z = ? rest = 410 x m o = 440 x m o - rest z = rest 30 x x = = 0.073

Worked Example 3 Consider again the Hydrogen line fromWorked Example nm recorded in the lab and 440nm observed from a star. b)Assuming the star is moving with a non- relativistic velocity, determine its recessional velocity. z = c = 3 x 10 8 ms -1 v  = ? v z = c v 3 x = v galaxy = x 3 x 10 8 = 2.2 x 10 7 ms -1

Worked Example 3 Consider again the Hydrogen line from Worked Example nm recorded in the lab and 440nm observed from a star. c)How does your answer compare with Worked Example 2c)? Answers are the same

Complete Problems from Tutorial IV The Expanding UniverseQ. 1 – 20 Answers 1.A = higher, B = lower, C D= Doppler Effect a) fo = fs b) fo = fs ms -1 v (v – v s ) v (v + v s )