Question

how can be calculate minimum distance for the hearing of echo

Answer 1

As the sensation of sound persists in our brain for about 0.1 s, to hear a distinct echo the time interval between the original sound and the reflected one must be at least 0.1s. If we take the speed of sound to be 344 m/s at a given temperature, say at 22 ºC in air, sound must go to the obstacle and reach back the ear of the listener on reflection after 0.1s.
 
Hence, the total distance covered by the sound from the point of generation to the reflecting surface and back should be at least (344 m/s) ×0.1 s = 34.4 m. Thus, for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be half of this distance. I.e., 34.4/2 = 17.2 m
[given speed of sound 344m/s]

Answer 2

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Echo➫ A repetition of the original sound heard after the sound is reflected from a distant, dense & rigid object.

Ex:- When we shout in front of a High Mountain or Deep Valley.

➧Derivation 0f An Echo (Minimum Distance):-▬▬▬▬▬▬▬▬▬▬▬▬☟

Speed = Distance Travelled / Time Taken

➧ Speed 0f Sound = 344 m/s
  (at 22◦C in Air)

➧ Time Taken = 1/10
  (Persistence 0f Hearing)

➧ Distance Travelled = ?

❱ Now, Put the Above Formula,

344 m/s = Distance / 1/10 sec
     D = 344 × 1/10
        = 34.4 m
        = 34.4 m / 2
        = 17.2 m ...✔

_________                Thanks...✊