B 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.
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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?
 
Thread 'Why higher speeds need more power if backward force is the same?'

Thread 'Why higher speeds need more power if backward force is the same?'

Power = Force v Speed Power of my horse = 104kgx9.81m/s^2 x 0.732m/s = 1HP =746W Force/tension in rope stay the same if horse run at 0.73m/s or at 15m/s, so why then horse need to be more powerfull to pull at higher speed even if backward force at him(rope tension) stay the same? I understand that if I increase weight, it is hrader for horse to pull at higher speed because now is backward force increased, but don't understand why is harder to pull at higher speed if weight(backward force)...
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