Question 261: Waves

Question

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second echo after 3 second. The distance between the two cliffs is (Velocity of sound $=340 \mathrm{~m} / \mathrm{s}$ )

Accepted Answer

A person stands between two parallel cliffs, fires a gun, and hears
two echoes
:
First echo after
1 second
Second echo after
3 seconds
Speed of sound $v = 340 \, \mathrm{m/s}$.
We want the distance between the two cliffs.
Step 1: Relation for echo
For an echo, sound travels from the person to the cliff and back.
So if distance from the person to a cliff is $d$, the round-trip distance is $2d$.
Echo time is
$ t = \frac{2d}{v}. $
So,
$ d = \frac{vt}{2}. $
Step 2: Find distances to the two cliffs
For the first echo ($t = 1 \, \mathrm{s}$):
$ d_1 = 	frac{340 	imes 1}{2} = 170 \, \mathrm{m}. $
For the second echo ($t = 3 \, \mathrm{s}$):
$ d_2 = 	frac{340 	imes 3}{2} = 510 \, \mathrm{m}. $
Step 3: Distance between cliffs
The person stands between cliffs, so one cliff is $170 \, \mathrm{m}$ away, the other is $510 \, \mathrm{m}$ away.
Thus, the
distance between the two cliffs
is
$ d_1 + d_2 = 170 + 510 = 680 \, \mathrm{m}. $
Ã¢ÂÂ Final Answer:
Option B: 680 m

Answer

340 m

Answer

680 m

Answer

1020 m

Answer

1360 m

Waves

A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and the second echo after 3 second. The distance between the two cliffs is (Velocity of sound =340 \mathrm{~m} / \mathrm{s} )

Choose the correct answer: