Sound: Speed-Solving Techniques (2)

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Tags Sound

Question

A man stands 170 m170\ \text{m} from a cliff and claps. He hears the echo 1 s1\ \text{s} later. What is the speed of sound in air? Solve in under 2020 seconds.

Solution — Step by Step

Echo problems are always round-trip. The sound travels from man to cliff and back, so total distance is 2d2d. We don’t write any wave equations.

v=2dt=2×1701=340 m/sv = \frac{2d}{t} = \frac{2 \times 170}{1} = 340\ \text{m/s}

Final answer: v=340 m/sv = 340\ \text{m/s}.

Why This Works

Echo questions are testing one idea: the round-trip factor of 22. Once you spot it, the algebra is one line. CBSE Class 9 boards repeat this pattern almost every year — only the numbers change.

For NEET, the same trick applies to SONAR (underwater echoes) and ultrasonic distance meters. Recognise the pattern, multiply by 22, divide.

Alternative Method

If the question gives speed and time, find distance: d=vt2d = \tfrac{vt}{2}. The factor of 22 is the only thing students forget — make it muscle memory.

For NEET-style questions involving two cliffs (echo from each side), use d1+d2=vt/2×2=vtd_1 + d_2 = vt/2 \times 2 = vt if echoes arrive simultaneously. This appeared in NEET 2021.

Common Mistake

Forgetting the round-trip and writing v=d/t=170 m/sv = d/t = 170\ \text{m/s}. This is the most common boards mistake — half the marks gone. Always draw a small arrow showing forward and return paths before computing.

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