-->

Mechanical Properties Of Fluids

Question
CBSEENPH11019127

The difference between the apparent frequency of a source of sound as perceived by an observer during its approach and recession is 2% of the natural frequency of source. Find the velocity of source. Take the velocity of sound as 350m/s.

Solution
The apparent frequency of wave perceived by observer when source of sound approaches the observer is, 
straight v subscript 1 equals fraction numerator straight V over denominator straight V minus straight u end fraction straight v                     ...(1) 
The apparent frequency of wave perceived by observer when source of sound moves away from the observer is, 
straight v subscript 2 equals fraction numerator straight V over denominator straight V plus straight u end fraction straight v                      ...(2) 
Change in the frequency of wave received is, 

          straight v subscript 1 minus straight v subscript 2 equals fraction numerator straight V over denominator straight V minus straight u end fraction straight v minus fraction numerator straight V over denominator straight V plus straight u end fraction straight v
   space space space space space space space space space space space space space equals fraction numerator 2 Vu over denominator straight V squared minus straight u squared end fraction straight v 
                    almost equal to fraction numerator 2 straight u over denominator straight V end fraction straight v                [∵ u<<V] 
Percentage change in frequency is, 
          fraction numerator straight v subscript 1 minus straight v subscript 2 over denominator straight v end fraction 100 equals fraction numerator 2 straight u over denominator straight V end fraction cross times 100 
It is given that the percentage change in frequency is 2%.
Therefore,
                 fraction numerator 2 straight u over denominator straight V end fraction cross times 100 equals 2 
rightwards double arrow             straight u equals straight V over 100 equals 3.5 straight m divided by straight s, is the velocity of the source.