Suppose you have a 2 meter long pole made of steel. Two persons hold both ends. Sometimes one person pushes it 10cm at 50km/h so that the other moves his arm. The other time one person hits it with a hammer blow of 50 km/h and the other person catches that blow with his hand. Does the movement/vibration reach the receiving person the same? It must have something to do with the speed of sound. Intuitively, a push seems to go faster, but is it?
Answer
Dear Loes,
I would do it like this: for both cases calculate (a) how long the interaction takes at one end of the rod and (b) how long it takes for the motion to reach the other side. Take the sum of both and see which sum is the smallest.
(1) Push
a. The speed decreases from 50 km/h to 0 km/h over a distance of 10 cm. This push takes approximately 10 cm / (25 km/h) = 4 * 10-6 u = 14.4 ms.
b. According to classical physics, the stick moves instantaneously (like a rigid object). (Or relativistically maximum at the speed of light. So this is negligible compared to the duration of the push. For the sake of completeness I’ll add it anyway: 2 m / (3 * 108 m/s) = 6.7 * 10-9 s.)
(2) Hammer strike
a. Information that seems to be missing: how long does the contact between hammer and rod last?
b. The speed of sound in steel is approximately 6 km/s. The time that the sound vibration travels to the other end is then 2 m / (6 km/s) = 0.34 ms.
The contact time between hammer and rod is probably much shorter than with the push. In that case, the sound vibration of the hammer blow arrives faster than the end of the push.
And since the speed of sound in steel is much higher than in air (about 340 m/s), the person at the other end will feel the hammer blow first and then hear it (after about 6 ms).
The intuition that the push is faster probably has to do with 1b, but this is only part of the story.
Regards,
Sylvia Wenmackers
Answered by
Prof. dr. Dr Sylvia Wenmackers
Philosophy of science, theoretical physics and materials physics.
Old Market 13 3000 Leuven
https://www.kuleuven.be/
.