-->

Mechanical Properties Of Fluids

Question
CBSEENPH11019088

Show that when source moves towards the stationary observer, the apparent increase in frequency is more than the apparent decrease in frequency if the source moves away from the source with same speed.

Solution
Let a source of sound be emitting the waves of frequency v.
Let V be the velocity of sound.
The apparent frequency of wave received by observer when source moves with velocity u is, 
            straight v subscript 1 equals fraction numerator straight V over denominator straight V minus straight u end fraction straight v        [moves towarads source] 
            straight v subscript 2 equals fraction numerator straight V over denominator straight V plus straight u end fraction straight v      [moves away from source] 
∴         space space space increment straight v subscript 1 equals straight v subscript 1 minus straight v equals fraction numerator straight u over denominator straight V minus straight u end fraction straight v                ...(1) 
and        increment straight v subscript 2 equals straight v subscript 2 minus straight v equals negative fraction numerator straight u over denominator straight V plus straight u end fraction straight v        ...(2) 
              fraction numerator open vertical bar increment straight v subscript 1 close vertical bar over denominator open vertical bar increment straight v subscript 2 close vertical bar end fraction equals fraction numerator straight V plus straight u over denominator straight V minus straight u end fraction 
rightwards double arrow            open vertical bar increment straight v subscript 1 close vertical bar space greater than space open vertical bar increment straight v subscript 2 close vertical bar 
Hence the result.