Question
A boy stands m from a tall wall and claps his hands. He hears the echo s later. Calculate the speed of sound in air on that day.
Solution — Step by Step
The clap sound travels from the boy to the wall, reflects, and returns. So the total distance covered by the sound is m, not m.
Speed = distance / time:
To the precision of the data, m/s. This is close to the standard textbook value of m/s at C; the slightly lower number suggests a cooler day.
Final Answer: m/s.
Why This Works
Sound travels in straight lines until it hits a surface, reflects, and returns. The “echo time” is the round-trip time, so the distance the sound covers is twice the boy-to-wall distance. This is the same logic SONAR and ultrasound use.
The speed of sound depends on temperature: it increases by roughly m/s per C rise. So the same experiment on a hot summer day in Chennai would give a slightly higher value than in a cool Delhi winter.
Alternative Method
Some textbooks set this up using “time for sound to reach wall = ”. The boy hears the echo when the sound completes the round trip, so each leg takes s. Then m/s. Same answer, slightly different framing.
The classic error: m/s. This forgets that the echo time covers a round trip. Half the speed of real sound — physically wrong, and an instant red flag if you sanity-check against the standard value of m/s.
For CBSE Class 9, examiners love asking the minimum distance for an echo to be heard distinctly: m, since the human ear distinguishes sounds separated by at least s and sound covers m in that time. Memorize this number.