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Problem Set 2 Solutions - Problem Set 2 Solutions Astronomy...

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Problem Set 2 Solutions Astronomy 201 Assigned: 13 Sep 2004 Due: 27 Sep 2004 Chapter 3: Review and Discussion: 2, 3, 13, 15, 18 2. Define the following wave properties: period, wavelength, amplitude, frequency. The wave period is a measurement of the amount of time needed for a wave to repeat itself at some point in space. The wavelength is the distance between any two consecutive positions in the wave, such as from peak to peak. The amplitude is the maximum height or depth of the wave above or below the undisturbed state. The wave frequency is the number of waves that pass a point per unit of time, usually waves per second. 3. What is the relationship between wavelength, wave frequency, and wave velocity? The relationship can be stated thus: the longer the wavelength, the lower the frequency; the shorter the wavelength, the higher the frequency. Wavelength and frequency are inversely related. Mathematically: wave speed = frequency * wavelength. 13. What is a blackbody? What are the main characteristics of the radiation it emits? A black body is an idealized object that absorbs all radiation falling on it. It also re-emits all this radiation. The radiation emitted occurs at all wavelengths but peaks at a wavelength that depends on the temperature of the black body. The hotter the temperature, the shorter the wavelength of the peak radiation. 15. What does Stefan’s law tell us about the radiation emitted by a blackbody? Stefan's Law relates the amount of radiation emitted by a black body to its temperature. The amount depends upon the fourth power of the temperature. Stated as an equation: E = σT 4 . E has units of energy per unit area, T is in Kelvins, σ = a constant with units of energy/unit area K 4 . 18. How do astronomers use the Doppler effect to determine the velocities of astronomical objects? By measuring the amount of shift in the wavelength of radiation, astronomers can determine whether an object is moving towards or away from us. The shift is proportional to the speed. So by measuring the Doppler shift, the velocity can be determined. Problems: 5, 6, 7, 10, 14 5. What would be the wavelength of an electromagnetic wave having a frequency equal to the clock speed of an 3.20 GHz personal computer? In what part of the electromagnetic spectrum would such a wave lie? Since λf = v and f = 3.2(10 9 ) Hz and v = 3(10 8 ) m/s we have: λ = 3(10 8 ) m/sec / 3.2(10 9 ) Hz = 0.094 m (short wave radio or long microwave). 1
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6. The blackbody emission spectrum of object A peaks in the ultraviolet region of the electromagnetic spectrum, at a wavelength of 200 nm. That of object B peaks in the red region, at 650 nm. Which object is hotter and, according to Wien’s law, how many times hotter is it? According to Stefan’s law, how many times more energy per unit area does the hotter body radiate per second?
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