Question

How far away is the cliff from the child, if a child hears an echo from a cliff $6seconds$ after the sound produced by powerful horn? The velocity sound in air at $22°C$ is $344m/s$.

Answer 1

Step 1: Given

The time when echo is heard after the sound is produced: $t=6s$

Velocity sound in air at $22°C$: $v=344m/s$

Distance between cliff and child is $d$

Step 2: Formula Used

The child hears an echo after producing the sound, so the sound travels two times the actual distance between the child and the cliff. Thus, the total distance the sound travels is $2d$.

Velocity is the ratio between the total distance and total time. Thus, $v=\frac{2d}{t}$.

Step 3: Solution

Calculate the distance using the formula.

$$\begin{gathered} v=\frac{2d}{t} \\ \Rightarrow 344=\frac{2d}{6} \\ \Rightarrow d=344\times \frac{6}{2} \\ \Rightarrow d=1032m \end{gathered}$$

Hence, the distance between the cliff and the child is $1032m$.