A person claps his hands near a cliff and hears the echo after 6 seconds. Taking the speed of sound v = 346 m/s, what is the distance of the cliff from the person (in metres)?

Introduction / Context:
This problem is about sound waves and echoes. When a person claps near a cliff, sound waves travel to the cliff, reflect and travel back to the person. The total time recorded is for the journey to the cliff and back. Using the known speed of sound, we can determine the one way distance to the cliff. This is a common type of question in physics related aptitude sections and connects motion concepts with wave phenomena.

Given Data / Assumptions:

Time between clap and echo = 6 seconds.
Speed of sound v = 346 m/s.
The sound travels from the person to the cliff and back (round trip) during these 6 seconds.
We assume air conditions are uniform so the speed of sound remains constant.
We need the distance from the person to the cliff (one way distance).

Concept / Approach:
The total distance covered by the sound wave during the echo is twice the distance from the person to the cliff, because the sound travels that distance going forward and the same distance returning. We first calculate the total distance using distance_total = speed * time. Then we divide this total by 2 to get the one way distance to the cliff. This is similar to round trip distance problems in time and distance topics.

Step-by-Step Solution:
Step 1: Compute total distance travelled by sound. distance_total = v * t = 346 * 6 metres. 346 * 6 = 2076 metres. Step 2: Find the one way distance to the cliff. distance_one_way = distance_total / 2 = 2076 / 2 metres. distance_one_way = 1038 metres.

Verification / Alternative check:
If the cliff is 1038 metres away, then a sound wave must travel 1038 metres to reach the cliff and another 1038 metres to return, giving a total of 2076 metres. At 346 m/s, the time taken for this round trip is distance_total / speed = 2076 / 346 seconds, which equals 6 seconds. This matches the information given in the question, confirming that 1038 metres is correct.

Why Other Options Are Wrong:
Option c (2076 m) represents the total distance travelled by the sound, not the distance to the cliff. Option b (1083 m) and option d (2706 m) do not satisfy the relation distance_total = 346 * 6 when doubled or halved appropriately. Only 1038 m is exactly half of 2076 m and corresponds to the correct one way distance when the round trip time is 6 seconds.

Common Pitfalls:
A common mistake is to forget that the sound travels to the cliff and back, leading some to use distance = speed * time directly as the distance to the cliff instead of the round trip distance. This gives 2076 m, which is double the correct value. To avoid this, always visualise the path: from the person to the reflecting surface and back, making it clear that the total distance is twice the one way distance.

Final Answer:
The cliff is 1038 m away from the person.