Expressions Of Pj Problems
Sound Travel In Iron

Sound Travel In Iron
The speed of sound in an iron rod is 16,850 ft/sec, and the speed in air is 1100 ft/sec. If a sound originating at one end of the rod is heard one second sooner through the rod than through the air, how long is the rod?

The string:
(a) S7P4A41 (Motion - Distancce);
The Math:
Sound Travel In Iron
Pj Problem of Interest (PPI) is of type motion. Problems of lengths unassociated with motion are generally of type containership. They are of type motion when associated with motion. In this scenario they are distances.
Above diagram is a sketch of the sound signal traveling in the rod (red signal) and in air (blue signal). We want to relate the speeds of the sound in air and in the rod to the length of the rod.
If it takes time t secs for the sound traveling inside the rod to transverse the rod
It will take time t + 1 secs for the sound to cover the same distance if traveling through air.
16850t = L ----(1)
1100(t +1) = L ----(2)
Therefore, 16850t = 1100(t +1)
So, 16850t -1100t = 1100
So, t = 0.0698secs.
Therefore, L = 0.0698(16850) = 1177 ft.


The point . is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.
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