If I had a solid metal bar say 1 mile long suspended in space. I hit one end with a hammer. How long before the energy reaches the other end? Would it be in relation to the speed of the hammer head when it was struck?
No it would not matter what speed the hammer is traveling at. What would matter the most is the density of the metal rod and its modulus of elasticity, ie its spring constant. But another thing affecting the problem you are describing, with a metal rod 1 mile in length, the metal’s own damping factor (very tiny value) would absorb the impact energy simply due to the sheer size of the rod. So in other words, the hammer impact energy may not even make it all the way to the other end. YMMV, and its difficult to say for sure without doing a specific analysis.
No. It will depend on the speed of sound of the material. This varies depending on the material.
Speed of sound for air at sea-level conditions is about 760 MPH.
Speed of sound for water is about 3300 MPH.
Speed of sound for steel is about 13,600 MPH.
Aluminum, 14,360 MPH.
So take your 1-mile-long steel bar, whack one end with a hammer; the vibrations will travel to the other end in 1/13,600 of an hour, or about 0.26 seconds. The airborne sound waves will cover that same distance in about 4.7 seconds.
If you hit your metal bar harder, the sound at the other end will be louder, but it won’t get there any faster.
The wave speed in an elastic rod is sqrt(E/rho) where E is the elastic modulus and rho is the density of the material.
My question was about metal because I figured more would be familiar with. I am trying to apply this somehow to measuring the hystrisis in various wood species. The idea was to form the wood into a dowel, suspend it by two strings and then tap one end while measuring the energy released at the other end. I am curious if using this method would give accurate predictions of hysterisis when bending wood such as in a bow and arrow. I still haven’t figured out what I would be measuring at the other end.
One test I was thinking of using was to hang two equal sized metal balls on opposite sides of the dowel and then dropping one, I would use a metal dowel for my base measure and then compare various species of wood by measuring how far the opposing ball traveled.
This question is much, much more complicated than the one about the steel rod. My suggestion would be to do actual experiments, using a setup as close as possible to the exact situation you’re interested in, and directly measure the quantity you’re interested in. In this case, that probably means making actual bows out of each of the woods, actually shooting arrows with each of them, and directly measuring how far the arrows fly.
I actually do make a lot of bows and have for many years. Possibly more than anyone else in the world considering all the species of wood I have worked with. My goal is to create a simple backyard test that any bow maker could use in his garage with no basic math involved. I have a whole series of tests I am working on that will be looking for specific characteristis of interest mainly to bow makers.
When we get a piece of wood we won’t have much left over and it would always be nice to know how to design around the specific wood I have in hand. We are mainly concerned with hysterisis and elasticity but are also concerned with tension and compressive strengths.