Doppler Effect and MathDate: 6/1/96 at 14:55:52 From: Anonymous Subject: Doppler Effect Dear Dr. Math, I am doing a research project for Algebra class on the Doppler Effect. My partner and I have done extensive research and gathered much information, but we are stumped on how the Doppler Effect is related to mathematics. The point of this project is to find the relevance between these two subjects, and we just can't figure it out. Please help us! Thanks, Brian and Tim Date: 6/1/96 at 19:27:39 From: Doctor Sarah Subject: Re: Doppler Effect Hi Brian and Tim - Here's part of an answer we sent out a while back to a question about the Doppler effect. Maybe you can use it to figure out more examples. "As an ambulance approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch. As the ambulance recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the ambulance is coming nearer or speeding away. If you could measure the rate of change of pitch, you could also estimate the ambulance's speed." Can you work out how this can be done? The whole answer can be found at: http://mathforum.org/dr.math/problems/rob5.19.96.html -Doctor Sarah, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 6/3/96 at 11:18:50 From: Doctor Mike Subject: Re: Doppler Effect Hello Doppler Questioner, Let me add to Doctor Sarah's answer. I'm glad you asked that question about what the Doppler Effect has to do with mathematics. Except for details, the answer is the same for any scientific subject area. Whenever you use an equation or a function to express the relationship between related things, you are using mathematics. The value in Dollars of a pile of Pennies is expressed by the equation D = P/100. Often this is expressed using the idea of a function, like D = H(P) where H is the "divide by 100" function. Science research results in theories about how things relate to each other. For the Doppler Effect, if the distance changes between you and a sound wave source, like the horn of a car driving past as you walk on a road, the sound frequency Fh that you "hear" depends on both the "true" sound frequency Ft, and also the Speed of the passing car. So, you get a conversion function Fh = C( Ft , Speed ) Your research should tell you what this equation is. You can then do interesting variants, such as how the equation changes if you aren't at the side of the road, but a block away. Graph these functions. Try to do a Science Fair demonstration showing Doppler Effect for water waves, which are the ones we can see directly. Try to get equations for other wave situations, like Red-Shift in astronomy, sonar, or Police radar speed detectors. I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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