Question

Minimum distance between the observer and the obstacle for echo to be heard.​

Answer 1

${\large{\underline{\underline{\mathfrak{Solution:-}}}}}$

Let distance between the observer and the obstacle = d

Speed of sound (in the medium) = v

Time after which echo is heard = t

$\fbox{\fbox{\large{\bold{Then,}}}}$

$t = \frac{2d}{v} \: or \: d = \frac{vt}{2}$

$\fbox{\fbox{\large{\bold{We\: know}}}}$

Speed of sound in air at 20°C

$= 343m \: \: {s}^{ - 1}$

For an echo to be heard distinctly,

$t \: \geqslant 0.1s$

$then \: \: \: d \geqslant \frac{343 m \: {s}^{ - 1} \times 0.1s }{2 \:} \: or \: \: d \geqslant 17.2m$

Thus, the minimum distance (in air at 20°C ) between the observer and the obstacle for the echo to be heard clearly should be 17.2 m.

Answer 2

Explanation:

An echo is heard only if the distance of the person sound from the rigid obstacles is long enough to allow the reflected sound to reach the person at least 0.1 second after the orginal sound .

We know that

D = V × Time / 2

by putting time = 0.1 and velocity = 340 m/ sec

Distance ( D ) = 340 × 0.1 / 2

= 17 meter

So , To hear an echo distinctly , the reflecting surface in air should be at minimum distance of 17 m from the listener.

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