Question

Trying to determine its depth, a rock climber drops a pebble into a chasm and hears the pebble strike the ground 3.54 s later.

(a) If the speed of sound in air is 343 m/s at the rock climber's location, what is the depth of the chasm? m

(b) What is the percentage of error that would result from assuming the speed of sound is infinite? %

Answer 1

(a) If the depth is d then the distance travelled by sound is 2d (d in going down and d in the journey back)

so we can write,

2d = 3.54x343=1214.22

therefore, d = 1214.22/2=607.11m

(b) we can write the fractional error in d as

so if v is infinite, then the first term on RHS becomes zero.

now for we can take error in the last digit. so

so

therefore percentage error is,