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  4. Two cars are moving on two perpendicuiar roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If first car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of second car when line joining the car makes angle of 45° with the roads, will be

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Q. Two cars are moving on two perpendicuiar roads towards a crossing with uniform speeds of 72 km/h and 36 km/h. If first car blows horn of frequency 280 Hz, then the frequency of horn heard by the driver of second car when line joining the car makes angle of $45^\circ$ with the roads, will be

ManipalManipal 1980Electromagnetic Waves

Solution:

The component of velocity of source along line joining
$ v_s = v_1 cos\, 45^\circ $
$ = 36 \times \frac{1}{\sqrt 2}km/ h $
$ = 5 \sqrt 2\, m/s $
Component of velocity of observer (second car) along line joining
$ v_0 =v_2\, cos\, 45^\circ =72 \times \frac{1}{\sqrt 2} km/h =10 \sqrt 2\, m/s$
$ n'= \frac{v + v_0}{v - v_s} n = \frac{330 + 10\sqrt 2}{300 - 5\sqrt 2} \times 280$
$ = \frac{344}{323} \times 280\, Hz = 298\, Hz$

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