A team of geophysicists is standing on the ground. Beneath their feet, at an unk

Question

A team of geophysicists is standing on the ground. Beneath their feet, at an unknown
distance, is the ceiling of a cavern. The floor of the cavern is a distance h below this ceiling. To
measure h, the team places microphones on the ground. At t = 0 s, a sound pulse is sent
straight downward through the ground and into the cavern. When this pulse reaches the ceiling
of the cavern, one part of it is reflected back toward the microphones, and a second part
continues downward, eventually to be reflected from the cavern floor. The sound reflected
from the cavern ceiling reaches the microphones at t = 0.0245 s, and the sound reflected from
the cavern floor arrives at t = 0.0437 s. The cavern is presumed to be filled with air at a
temperature of 9 °C. Assuming that air behaves like an ideal gas, what is the height h of the
cavern?

Explanation / Answer

extra distance traveled by wave reflected from floor of ceiling = 2h time taken for sound wave to travel this distance = 0.0192 s speed of sound wave in air = 331.5 + 0.6T = 336.9 m/s h = 3.234 m

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