High School Understanding the Doppler Effect at an Angle

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The Doppler effect formula for sound when the source and observer are moving at an angle involves adjusting the standard formula to account for the angle of approach or recession. The frequency observed can be calculated using the cosine of the angle between the source's direction and the line of sight to the observer. Various resources discuss the implications of this angle on perceived frequency changes, emphasizing the need for vector components in calculations. Understanding these adjustments is crucial for accurate predictions in real-world scenarios, such as in acoustics or radar technology. Mastery of the Doppler effect at an angle enhances comprehension of sound wave behavior in dynamic environments.
abdossamad2003
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hello everyone
How is the sound Doppler effect formula in the case where the movement of the source and the observer is at an angle?
 
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What have you found so far in your reading about the Doppler effect?
 
Topic about reference frames, center of rotation, postion of origin etc Comoving ref. frame is frame that is attached to moving object, does that mean, in that frame translation and rotation of object is zero, because origin and axes(x,y,z) are fixed to object? Is it same if you place origin of frame at object center of mass or at object tail? What type of comoving frame exist? What is lab frame? If we talk about center of rotation do we always need to specified from what frame we observe?

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