Question

You are hiking along a trail in a wide, dry canyon where the outdoor temperature is T = 29.5° C. To determine how far you are away from the canyon wall you yell "Hello" and hear the echo t = 1.8 s later.

Answer 1

Answer:

The canyon is approximately 314 meters away

Explanation:

Speed of Sound

If we emit sounds in an open space where a large obstacle (like a mountain) is expected to return the sounds, then it will travel forth and back at a given speed for a certain time. We can assume the speed of sound is constant, so we could know the approximate distance of the mountain (or canyon in our case) by the known formula.

$x=v_st$

Where $v_s$ is the speed of sound and t is half the time we hear our echo.

The speed of sound in m/s can be calculated from the approximate formula in terms of the temperature T in degrees Celsius

$v_s=331.3+0.606T$

We have $T=29.5^oC$, so

$v_s=331.3+0.606(29.5)$

$v_s=349.177\ m/s$

Let's compute x, for t=1.8/2=0.9 seconds

$x=v_st=(349.177)(0.9)$

$x=314.26\ m$

The canyon is approximately 314 meters away