Question
What is an echo? What is the minimum distance from a wall required to hear a distinct echo? (Take speed of sound = 344 m/s at 20°C)
Solution — Step by Step
When sound hits a hard surface — a cliff, a building, a large wall — it bounces back. If this reflected sound reaches our ears after a noticeable delay, we hear it as a separate sound. That’s an echo.
Our ears cannot distinguish two sounds that arrive less than 0.1 seconds apart. This 0.1 s limit is called the persistence of hearing. So for an echo to be heard distinctly, the reflected sound must return at least 0.1 s after the original sound.
Sound travels from us to the wall and back — total distance = 2d, where d is our distance from the wall. Using the relation:
So we must stand at least 17.2 metres from the reflecting surface to hear a distinct echo.
NCERT Class 8 uses 344 m/s at 20°C. Some older textbooks use 340 m/s, giving d = 17 m. Both are acceptable — mention the speed you’re using. The board exam typically gives the speed in the question itself.
Why This Works
The key idea is that our ears work like a buffer — sounds that arrive within 0.1 s of each other get “merged” and heard as one. This is the same reason we perceive cinema as smooth motion rather than a series of frames.
The reflecting surface must be large, hard, and smooth — a cliff face works well, but a curtain doesn’t. Soft materials absorb sound instead of reflecting it. This is why your voice echoes in an empty hall but not in a furnished room.
At 20°C (v = 344 m/s): = 17.2 m
At 0°C (v = 332 m/s): ≈ 16.6 m
Alternative Method
Some students prefer thinking in terms of round-trip time directly.
The sound takes 0.1 s to complete a round trip (to wall and back). So in 0.05 s, sound covers the one-way distance:
Same answer, fewer steps. This approach — splitting the time in half from the start — avoids writing the 2d equation and is slightly faster in MCQs.
In JEE-style numerical problems, speed of sound is given at a specific temperature. For CBSE Class 8 and 9 boards, just remember: 17.2 m at 20°C is the standard answer.
Common Mistake
Students forget to divide by 2 and write d = 34.4 m directly. The sound travels to the wall and back — total path is 2d, not d. Always draw a quick sketch: you → wall → you. The 34.4 m is the total round-trip distance, not the distance to the wall.
Another trap: using t = 1 s instead of t = 0.1 s. The persistence of hearing is one-tenth of a second, not one full second. This mistake gives d = 172 m, which is off by a factor of 10 — easy to catch if you have any physical intuition for how far 17 m actually is.