Question

problem 5: while visiting the grand canyon, you start speaking loudly near the cliff side. the face of the cliff is 0.28 km away. how long does it take for you to hear your own echo?

Explanation:

Step1: Convert distance to meters

The distance to the cliff is \(d = 0.28\space km=0.28\times1000\space m = 280\space m\). The sound travels to the cliff and back, so the total distance \(s = 2d=2\times280\space m = 560\space m\).

Step2: Use the formula \(v=\frac{s}{t}\) to find time

The speed of sound in air \(v = 343\space m/s\). Rearranging the formula \(t=\frac{s}{v}\), substituting \(s = 560\space m\) and \(v = 343\space m/s\), we get \(t=\frac{560}{343}\space s\approx1.63\space s\)

Answer:

It takes approximately \(1.63\space s\) to hear the echo.