# Blending of Doppler's Effect and Calculus

**Classical Mechanics**Level 5

Consider an Standard Cartesian Coordinate system (X-Y plane). If An Sound Source is moving on a parabolic Path \(\displaystyle{{ y }^{ 2 }=4x}\) with constant speed \(\displaystyle{{ v }_{ s }=\cfrac { v }{ 2 } }\) . Here \(v\) is velocity of sound in still air.

At time t=0 the source is at the origin , and an Observer is standing at rest at the position whose coordinates are \(\displaystyle{(-1,0)}\) . Then Find the time interval in which observer Hears the **minimum** frequency of sound. If this time interval can be expressed as :
\[\displaystyle{T=\cfrac { a\sqrt { b } +c\ln { (\sqrt { d } +e) } }{ v } }\]

Find \(a+b+c+d+e\) .

Here \(a,b,c,d,e\) are positive integers , and \(b,d\) are square free integer .

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###### Try such more Deepanshu's Mixing of concepts

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