Exam code: YPH11
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Define Doppler effect.
The Doppler effect (or Doppler shift) is the apparent shift in wavelength occurring when the source of the waves is moving.

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What happens to the wavelength and frequency of waves observed in front of, and behind, a moving wave source?
In front of the source: wavelength decreases (λ – Δλ) and frequency increases
Behind the source: wavelength increases (λ + Δλ) and frequency decreases
Does the wavelength emitted by a moving source itself change?
No. The actual wavelength emitted remains the same — only the wavelength received by the observer appears to have changed.
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Define Doppler effect.
The Doppler effect (or Doppler shift) is the apparent shift in wavelength occurring when the source of the waves is moving.
What happens to the wavelength and frequency of waves observed in front of, and behind, a moving wave source?
In front of the source: wavelength decreases (λ – Δλ) and frequency increases
Behind the source: wavelength increases (λ + Δλ) and frequency decreases
Does the wavelength emitted by a moving source itself change?
No. The actual wavelength emitted remains the same — only the wavelength received by the observer appears to have changed.
A stationary wave source produces wavefronts that spread out .........., whereas a moving source causes them to appear squashed in front and stretched behind.
A stationary wave source produces wavefronts that spread out symmetrically, whereas a moving source causes them to appear squashed in front and stretched behind.
True or False?
The Doppler effect can only be observed using sound waves.
False.
The Doppler effect can be observed using any form of electromagnetic radiation, not just sound — for example, by comparing the light spectra of nearby and distant galaxies.
What does redshift in the light spectra of distant galaxies provide evidence for?
Redshift provides evidence that the universe is expanding.
Define redshift.
Redshift is the fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other.
State the equation used to calculate Doppler redshift for a non-relativistic galaxy, and define each symbol.
Δλ = shift in wavelength (m)
λ = wavelength emitted from the source (m)
Δf = shift in frequency (Hz)
f = frequency emitted from the source (Hz)
v = speed of recession (m s-1)
c = speed of light in a vacuum (m s-1)
State Hubble's law in words.
The recessional velocity of a galaxy is directly proportional to its distance from Earth.
Hubble's law can be expressed as , where H0 is the ...........
Hubble's law can be expressed as , where H0 is the Hubble constant.
True or False?
According to Hubble's law, galaxies further from Earth move away more slowly than closer galaxies.
False.
Hubble's law shows the opposite — the furthest galaxies move away the fastest.
If v is measured in km s-1 and d is measured in km, what is the unit of the Hubble constant, H0?
s-1
Define dark matter.
Dark matter is matter which cannot be seen and does not emit or absorb electromagnetic radiation.
State the equation used to calculate the Hubble constant, H0, from recessional velocity and distance.
What is the latest Planck satellite estimate of the Hubble constant, including its uncertainty and units?
H0 = 67.4 ± 0.5 km s-1 Mpc-1 (Planck Collaboration VI, 2020).
Why is it difficult to be certain how accurate values of the Hubble constant are?
Because of the random and systematic errors involved in measuring the distance to a galaxy or star.
In galaxies, the orbital velocity of stars does not .......... with increasing distance from the centre, unlike in smaller systems such as the solar system.
In galaxies, the orbital velocity of stars does not decrease with increasing distance from the centre, unlike in smaller systems such as the solar system.
True or False?
All of the observable mass of a galaxy is concentrated in the same way as its total mass, including dark matter.
False.
All of the observable mass of a galaxy is concentrated in its centre, but its total mass (including dark matter) is spread out — this mismatch is why dark matter is inferred to exist.
How is dark matter detected, given it cannot be observed directly through telescopes?
By its gravitational effects — either the rotation of galaxies or the gravitational lensing of starlight.
What proportion of the mass of the universe is thought to be made up of dark matter?
Approximately 27%.
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