Objetives/Key Points Module 5: Red Reedes, Blue Approahes UNC-TFA H.S. Astronomy Collaboration, Copyright 2012 Students will be able to: 1. math the diretion of motion of a soure (approahing or reeding) with the apparent sensory effet (olor, pith) and the hange in wave properties (higher/lower frequeny, shorter/longer wavelength). To failitate this goal, students will memorize the mnemonis red is reeding and low is long. 2. use the language of redshift and blueshift. 3. identify the extra mathematial term that distinguishes the Doppler shifted wavelength from the wavelength emitted by the soure. 4. apply the Doppler shift formula (derived together) to determine either the motion of objets or the hange in the wavelength/frequeny, when given one or the other. Unit Home Waves Prerequisites Students should be familiar with waves, both sound and eletromagneti, but need not have been exposed to Doppler shifts. The preparatory homework for this lass introdues the Doppler shift equation. Time: (20 min. prep; an be homework +) 60 min (+ 20 min enrihment) Materials video found at http://www.youtube.om/wath?v=imoxdn2sgo if doing enrihment, an use gas tubes and gratings/spetrometers opies of advane homework worksheet and in-lass worksheet Stiking Points 1. Students tend to onfuse higher/lower pith with louder/softer sound and thus loser/further. Pre-Lesson Advane Preparation for Lesson: Have students omplete appended worksheet as homework. Remind them of terminology of fator and ratio before giving it. At the start of the main lass, go over onept heks at the end of this homework then omplete appended quiz. Main Lesson 1. Fire truk video revisited and disussed with hart below (teaher helps with left olumn, students try right olumn then disuss). Teaher mention mnemonis and put on blakboard: red is reeding and low is long. Go over quiz/homework problem 1.
In-Class Worksheet Fire Truk Approahing Fire Truk Reeding Drawing Drawing The pith of the siren is. (higher/lower) The pith of the siren is. (higher/lower) The frequeny is, and therefore the wavelength is. (higher/lower), (longer, shorter) The frequeny is, and therefore the wavelength is. (higher/lower), (longer, shorter) If this were a light wave, the light wave would be. (red shifted/blue shifted) If this were a light wave, the light wave would be. (red shifted/blue shifted) Equation Derivation Spae
Independent Pratie 2. Students omplete the following individually in lass. Teaher reinfores mnemonis red is reeding and low is long. Sensory Effet on Observer (lower/higher pith or redshifted/blueshifted olor) Motion (approahing, reeding) Wavelength/Frequeny (longer or shorter/lower or higher) lower pith longer/ pith Approahing / pith /lower pith getting er reeding faster and faster getting er/ er Redshifted Reeding / Blueshifted / longer/ /higher Presentation & Conept Cheks (integrated) 3. Teaher derives Doppler shift formula on blakboard reiterating handout in Sorati style and also taking questions. This derivation is a review of the material in the homework, so the students should be able to help lead it. Class goes over homework/quiz problem 2. 4. Teaher role models appliation of formula by going over homework problem 3. Independent Pratie (an beome Homework if time runs out) 5. Try the following problems in lass with teaher irulating. a) Suppose the wavelength of an approahing star hanges by a fator of 1.0001. Write an equation relating λ to λ, thinking about whether the wavelength inreases or dereases. Using the Doppler shift equation, what is the veloity of the star? Is the sign of the veloity you derived orret and why? Is this a redshift or a blueshift? b) Suppose a star is reeding at a veloity of 100 m/s. Calulate the hange in the ratio of λ to λ. Is this a redshift or a blueshift? Is your ratio onsistent with a reeding star, and why?
Enrihment If the spetrum of a star inludes a full rainbow of olors, it is not easy to see the Doppler shift in the overall olor of the star (whih is just the brightest olor range in a spetrum of olors). The overall olor shift is only large enough to notie for distant galaxies that are expanding with the osmi expansion of the Universe, moving muh faster than nearby stars. So how do we tell that nearby stars have Doppler shifts? Disuss lines in spetra and how they an be used as signposts to atually measure wavelength shifts and therefore veloities of light-emitting objets. Homework (or an serve as Assessment) 1. What if a star is orbiting another star at a speed of 30 m/s; how will its Doppler shift hange with time? How big is the hange in wavelength? Assume the observer is wathing the stars orbiting edge on, so that one star is going in front of and behind the other periodially.
Doppler Shifts: Advane Preparation Worksheet Often, the information that we reeive from objets (in the form of light or sound) is not true to the information that left the objet. For example, let s think about the way a fire truk sounds to the person driving the truk versus a person standing on the side of the road as the truk drives by. To the person in the truk, the sound of the siren is a onstant frequeny. Therefore the driver hears a onstant pith, true to the atual pith of the siren. Now the person on the side of the road hears something a little different. Wath the video in lass, whih an also be found at http://www.youtube.om/wath?v=imoxdn2sgo. As the truk is oming towards the person on the side of the road, the frequeny is being altered. The sound wave is moving with its initial speed as well as the speed of the truk. This auses the wave to be shortened making the frequeny or pith seem higher. As the truk is driving away from the person on the side, the opposite happens. The sound wave is moving with the initial speed minus the speed of the truk. Therefore, to the person on the side of the road, the sound wave seems to be strethed making the frequeny or pith seem lower. The hange in the frequeny (or equivalently, wavelength) of the wave ompared to its emitted value is alled a Doppler shift. Now let s examine the Doppler shift for the light given off by a star that is moving away from an astronomer, whih hanges the olor of the light. We know that the equation for the speed of a wave is given by v = λ f. For light, this equation beomes = λ f. The wavelength of light as emitted by the star is λ = f. Reall that one wavelength is the length between two wave rests. Therefore if t = λ is the time between the emission of the
rests, then the first rest to be emitted has traveled a distane d wavemotion = λ = t in that time. From the point of view of the star, this is the only motion, so the seond rest follows the first at distane λ and the wavelength is what we expet. But from the point of view of the astronomer, the star has moved a distane d = v t so the seond rest follows the first at distane d wavemotion starmotion star starmotion star + d = t + v t = λ. Thus when we look at the star we find that the wavelength of light is atually strethed or λ longer than the light wave emitted. Realling that λ = t and t =, we λ have λ = λ + vstar. The Doppler shift equation is then v λ = + star λ 1 where the veloity is defined as positive when reeding. v In the piture above, the green wave represents the light given off by the star. As the star moves away from the observer, the wave is strethed and the observer sees the wave as being red. This is what is known as a redshift. It tells us that an objet is moving away from us. Using the above equation, we ould figure out the relative speed between us and the star. Stars an also being moving towards us, similar to the fire truk example. Of ourse this would make the wavelength appear shorter, making it appear bluer. This is referred to as a blueshift. Conept Cheks: 1. If a fire truk is moving (fill in toward or away from) you, the pith is inreasing, whih is analogous to a (fill in redshift or blueshift) for starlight if the star is (fill in approahing or reeding). 2. The wavelength of light or sound from an approahing objet (star, fire truk) will be (fill in longer or shorter). If the veloity of approah is v 1 (a positive number), then what is the equation for the wavelength? Cirle the extra term that modifies the wavelength. Should the extra term be positive or negative? 3. For a reeding star, suppose the wavelength inreases by a fator of 1.0001, i.e., λ = 1. 0001. Using the Doppler shift equation, what is the veloity of the star? λ
Quiz: 1. If a fire truk is moving (fill in toward or away from) you, the pith is dereasing, whih is analogous to a (fill in redshift or blueshift) for starlight if the star is (fill in approahing or reeding). 2. The wavelength of light or sound from a reeding objet (star, fire truk) will be (fill in longer or shorter). If the veloity of reession is v (a positive number), then the v equation for the wavelength is λ = + star λ 1. Cirle the extra term that modifies the wavelength. Should the extra term be positive or negative? Answers to Conept Cheks: 1. toward, blueshift, approahing v 1 2. shorter, λ = λ 1 sine the veloity is approahing, extra term is v λ 1, whih should be negative in order to make the wavelength smaller (shorter/bluer) than the 3. If λ = 1. 0001λ then 1+v/ = 1.0001 for v defined as positive sine the star is reeding. Thus v = 0.0001 = 30 km/s. Answers to Quiz: 1. away from, redshift, reeding v star 2. longer, extra term is λ, whih should be positive in order to make the wavelength larger (longer/redder) than the, sine the objet is reeding