Astronomy 2, Spring 2007

Homework set 4, due May 8 .

1. Waves.

(a) What is the relationship between wavelength, frequency, and speed of a wave?

(b) While surfing you notice that the speed of the waves is 10 m/s and that a wave crest passes a buoy every 10 seconds. What is wavelength of the waves?

(c) Waves travel down a string at 1 m/s with a distance between crests of 30 cm. What is the frequency of the waves?

(d) Unlike light waves, sound waves are traveling waves of compression and rarefaction of the medium through which they are passing. Suppose a musician 10 m away from you struck a tuning fork . You simultaneously dashed away from the tuning fork at the speed of sound (you move fast!). Would you hear the tuning fork at a lower or higher frequency or perhaps not hear it at all? Explain.

2. Doppler effect.

(a) The Andromeda Galaxy is the nearest large galaxy to ours. It is about 750,000 pc away. If hydrogen gas in the Andromeda Galaxy emits radiation at a wavelength of 656.3 nm, but we observe it at 649.7 nm, calculate how fast is the galaxy moving with respect to us. The speed of light is 3x10⁵ km/s.

(b) Is the Andromeda Galaxy moving toward or away from us? Explain.

(c) If the Andromeda galaxy were 1.5 million pc from us, what would the Doppler shift be, assuming all else is the same?

(d) What does the Doppler effect tell us about how fast the Andromeda Galaxy is moving through space relative to our galaxy, that is, its total motion that is a combination of motions along the line of sight and perpendicular to it.

3. Kirchoff’s spectral laws. These laws describe physical conditions that give rise to three basic kinds of spectra: continuous, emission, and absorption spectra. Using your understanding of these laws, identify which kind of spectrum you would expect to observe in the following conditions. Explain your answers.

(a). A cauldron of molten iron (as in a steel mill).

(b) The same cauldron viewed through a cloud of hot (though cooler than the cauldron) sodium gas.

(c) A cloud of hot sodium gas with nothing behind it.

(d) A mercury vapor street lamp.

(e) An incandescent (tungsten filament) desk lamp.

(f) A glowing wire in a toaster.

(g) A neon sign

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