If you shout across a canyon and hear an echo 3.3 s later, how wide is the canyon?

Question

If you shout across a canyon and hear an echo 3.3 s later, how wide is the canyon?

_____m

it is NOT 1.65m

Answer 1

The speed of sound in air is:

331.4 + 0.6T(c)

Where T(c) is the temperature in degrees Celsius.

Since the sound travels across the canyon and back the time is:

3.3 s / 2 = 1.65 s

(331.4 + 0.6T(c)) m/s * 1.65 s = the width of the canyon

Answer 2

The speed of sound is generally accepted to be about 340.3 meters/second at sea level.  If we use that number then the sound traveled a total distance of 3.3 x 340.3 = 1123 meters, which is the "out and back" distance.  The canyon would be 1/2 that width or about 561.5 meters wide.

Answer 3

let cannon be x m wide

so total distance covered by sound = x+x ( while going and returning) =2x

speed of sound = 340 m/s

S=D/T

340=2x/3.3s

x=561 m ( approx )  

Answer 4

Assume 343 m/s for the speed of sound in air (correct for dry air at 20 degrees C).

The sound therefore travels 343 m/s * 3.3 s = 1132 m (approximately).

This is a round trip across the canyon, hence the width of the canyon is half that, or 566 m.