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Mechanical Properties Of Fluids

Question
CBSEENPH11019102

A car approaching with velocity u towards the stationary observer crosses past him. What is the apparent change in frequency of the note when car is crossing the observer?

Solution
Consider,
v = frequency of note, and
V =  velocity of note in air.
The apparent frequency of note while car is approaching before crossing, 
                straight v subscript 1 equals fraction numerator straight V over denominator straight V minus straight u end fraction straight v 
The apparent frequency of note after crossing, 
                 straight v subscript 2 equals fraction numerator straight V over denominator straight V plus straight u end fraction straight v 
The change in the apparent frequency of note on crossing, 
                   increment straight v equals straight v subscript 2 minus straight v subscript 1
                       equals open parentheses fraction numerator straight V over denominator straight V plus straight u end fraction straight v close parentheses minus open parentheses fraction numerator straight V over denominator straight V minus straight u end fraction straight v close parentheses
                      space space equals negative fraction numerator 2 uV over denominator straight V squared minus straight u squared end fraction straight v