Show that the reflector must be situated at a least distance from the observer for formation of distinct echo. What is the value of this distance at room temperature?

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

The sensation of sound, which an observer hears, persists in the brain for about 0.1 s. Thus, for distinct echo formation, the time difference between the original sound and reflected sound must be at least 0.1 s or more.

Now, the time of echo is t = 2d/v, where d is the distance between observer and the reflecting surface and v is the velocity of sound.
Hence, d  = vt/2
Therefore, minimum distance (d) = v x 0.1/2 = v/20
Thus, reflector surface must be situated at a minimum distance of v/20 in order to form a distinct echo.
At room temperature of about 22oC speed of sound in air has a value of 344 m s-1, hence value of minimum distance (d) = 344/20 = 17.2 m
It means that in a room of length less than 17.2 there will be no echo. 

Answered by  | 4th Jun, 2014, 03:23: PM