Question 494: Waves

Question

A person is standing at some point between two parallel cliffs (not exactly at the centre). He claps, and hears two echoes: the first after $$1 \mathrm{~s}$$ and the second after $$2 \mathrm{~s}$$. If the speed of sound in air is $$330 \mathrm{~m} / \mathrm{s}$$, the distance between the two cliffs is

Accepted Answer

Let the two cliffs be
A
and
B
, and let the person be at a point
P
between them.
Let the distance of the person from cliff
A
be $ x $ metres and from cliff
B
be $ y $ metres.
Step 1: Understanding the time for echoes
The sound travels from $ P $ to a cliff and back to $ P $.
Therefore, the total distance covered by the sound is $ 2x $ for the echo from cliff
A
, and $ 2y $ for the echo from cliff
B
.
Given,
Time for first echo $ t_1 = 1 \, 	ext{s} $
Time for second echo $ t_2 = 2 \, 	ext{s} $
Speed of sound $ v = 330 \, 	ext{m/s} $
Step 2: Using the relation $ 	ext{Distance} = 	ext{Speed} 	imes 	ext{Time} $
For first echo:
$ 2x = v 	imes t_1 = 330 	imes 1 = 330 $
$ \Rightarrow x = 165 \, 	ext{m} $
For second echo:
$ 2y = v 	imes t_2 = 330 	imes 2 = 660 $
$ \Rightarrow y = 330 \, 	ext{m} $
Step 3: Finding the distance between the two cliffs
The total distance between the two cliffs is
$ x + y = 165 + 330 = 495 \, 	ext{m} $
Step 4: Final Answer
The distance between the two cliffs is
$ \boxed{495 \, 	ext{m}} $
Hence, the correct option is
Option B (495 m)
.

Answer

330 m

Answer

495 m

Answer

660 m

Answer

990 m

Waves

A person is standing at some point between two parallel cliffs (not exactly at the centre). He claps, and hears two echoes: the first after $1 \mathrm{~s} and the second after 2 \mathrm{~s}. If the speed of sound in air is 330 \mathrm{~m} / \mathrm{s}$, the distance between the two cliffs is

Choose the correct answer: