Tag: reflection of sound and echo

The minimum distance in air between the observer and the obstacle for an echo to be heard clearly at temperatures higher than ${25}^{0}C$ is more than $17.2m$. The speed of sound increases with rise in temperature.

For the production of an echo, the reflecting surface or the obstacle should be rigid such as building, hill, cliff etc.

The human ear can hear two sounds distinctly only if there is a time interval of $\frac{1}{10}$seconds between them. Now, the speed of sound in air at $20^0$C is $340m/s$, so the distance traveled in $\frac{1}{10}$seconds will be: 
Distance = Speed X time 
$=340 \times \frac{1}{10} \= 34m$

Thus, it is possible to hear the echo at the minimum distance of $\frac{34}{2}= 17m$ between the source of sound and reflecting surface. 

Minimum frequency to the human ear is 20
$\therefore T= \dfrac {1} {F}$
$T=\dfrac{1} {20}$
$d= V \times t$
$d= V\times \dfrac {1} {20}$
$\therefore$ The minimum distance is$ \dfrac {V} {20}$, where V is speed of the sound.

Let the distance between the two cliffs be d. Since, the man is standing midway between the two cliffs, then the distance of man from either end is $d/2$.
The distance travelled by sound (in producing an echo)
$2\times \displaystyle\frac{d}{2}=v\times t\Rightarrow d=340\times 1=340$m.

The echo of the first signal will overlap with the second signal. Thus, an echo will not be absent

Distance required for an echo to be heard is 17 m. Thus, $17 =  0 + \dfrac{0.5 t^2}{2} \implies t= 2\sqrt{17}=8.2 s$. 

The correct option is (b)

To hear an echo, the distance between the source and the reflector should be atleast 17 m. Thus the source should be moved 7 m away from the wall

The correct option is (b)

distance moved by the source = 17 m for the echo to be heard

Thus, $17 = v(4) \implies v = 17/4 = 4.25 $ m/s

The correct option is (c)

to hear echo of a sound the minimum distance between source and reflecting surface should be 17m.