Physics
Physics
Problem
On a clear summer evening the speed of sound in air is measured to be at . A boy standing on level ground claps his hands once and waits for an echo from a tall wall directly in front of him. (a) Calculate the minimum distance of the wall from the boy so that he can hear a distinct echo. (b) The temperature rises uniformly to , for which the speed of sound increases by per degree Celsius rise. Determine again the minimum distance required under the new conditions.Intuitive explanation
The key to hearing a distinct echo is understanding the persistence of hearing: your ear can only distinguish a sound as separate from the original if it arrives after a minimum time delay (typically around 0.1 s). Since sound must travel to the wall and back, you need to find the distance that gives this round-trip time. In part (b), a warmer temperature speeds up sound, so the same distance gets covered faster—meaning you need to go farther to maintain that critical time delay.
Intuitive explanation
The key to hearing a distinct echo is understanding the persistence of hearing: your ear can only distinguish a sound as separate from the original if it arrives after a minimum time delay (typically around 0.1 s). Since sound must travel to the wall and back, you need to find the distance that gives this round-trip time. In part (b), a warmer temperature speeds up sound, so the same distance gets covered faster—meaning you need to go farther to maintain that critical time delay.