A boy receives the echo of his clap reflected by a nearby hill 0.8s later. If the speed of sound in air is 340ms$^-1$, how far is he from the hill?

Analysis

The question asks for the distance between a boy and a hill, given the time it takes for an echo to return and the speed of sound. An echo occurs when sound travels to an object (the hill) and reflects back to the source (the boy).

Concept

The formula for speed is:

In the case of an echo, the sound travels to the hill and back to the boy. Therefore, the total distance covered by the sound is twice the distance between the boy and the hill ($2d$). The formula becomes:

Solution

Step 1: Identify the given values.

• Speed of sound ($v$) = $340 \, \text{ms}^{-1}$
• Time ($t$) = $0.8 \, \text{s}$
• Distance ($d$) = ?

Step 2: Rearrange the formula to solve for $d$.

Step 3: Substitute the values into the equation.

Conclusion

The boy is 136 meters away from the hill.

Exam Tip

Always remember that for echo problems, the sound must make a "round trip." If you forget to divide by 2, you will get 272m (which is option C), a common distractor in JAMB questions. Always ask yourself: "Did the sound travel there and back?" If yes, divide your final distance by 2!