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Mechanical Properties Of Fluids

Question
CBSEENPH11019060

A man standing between two parallel cliffs clap and hears two echoes, one 2-4s and second at 3.6s after clapping. If the velocity of sound is 340m/s, find the distance between the two cliffs.

Solution
Let the man be at a distance of d1 from one cliff and d2 from the other cliff.
The first echo is heard after reflection from the first cliff and the second reflection is heard after reflection from the second cliff. 

As the first echo is heard at time t1 = 2.4s,
∴            2 straight d subscript 1 equals vt subscript 1 
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∴             2 straight d subscript 2 equals vt subscript 2 
               space space space straight d subscript 2 equals vt subscript 2 over 2 equals fraction numerator 340 cross times 3.6 over denominator 2 end fraction equals 612 straight m 
 Thus, the distance between two cliffs is given by, 
     straight d equals straight d subscript 1 plus straight d subscript 2 equals 408 plus 612 equals 1020 straight m