An old mining tunnel disappears into a hillside. You would like to know how long
ID: 1574857 • Letter: A
Question
An old mining tunnel disappears into a hillside. You would like to know how long the tunnel is, but it's too dangerous to go inside. Recalling your recent physics class, you decide to try setting up standing-wave resonances inside the tunnel. Using your subsonic amplifier and loudspeaker, you find resonances at 4.5 Hz and 6.3 Hz, and at no frequencies between these. It's rather chilly inside the tunnel, so you estimate the sound speed to be 335 m/s. Based on your measurements, how far is it to the end of the tunnel? Assume the tunnel is blocked at the other end.
For full credit, you must show your work and explain whether your answer seems reasonable.
Explanation / Answer
The tunnel will act as a pipe closed at one end
The different frequencies for a pipe closed at one end are V/4L, 3V/4L,5V/4L,7V/4L ...
so the difference between any two consecutive frequies= f2-f1=2V/4L
6.3-4.5= 2(335)/4L
L= 93 m