Do Solid and Hollow Metal Rods Produce Different Standing Wave Patterns?

[klng]

Hello friends,

I have done some research on the Internet about producing standing waves in a metal rod, and how the various harmonics frequencies are being derived. I have two questions that i wish to discuss here:

1. Is the pattern of standing waves and method of formula derivation the same, even when we use a solid metal rod, i.e. the rod is filled in the centre, as opposed to a hollow tube?

2. When we strike the rod at one end, we should do so by striking the rod longitudinally, i.e. the hammer strikes the face of the rod end. Only then will standing waves be formed, and we can derive our harmonics frequencies formula (depending on where we hold the rod). My question is, what happen if we strike the end in a transverse manner, i.e. we strike the hammer across the end of the rod. Will there be any pattern of standing waves being formed, and can we derive a formula to determine the harmonics frequencies? Apparently, there seems to be such a formula, though i can't figure out how it was being derived. Pls refer to this link, look under the bold header "Extensions, other activities using the bar":
http://www.exo.net/~pauld/summer_institute/summer_day11sound/ringing _Al_rod.html.
There is a table of values there, associated with the various harmonics.

Hope experienced forummers can help shed some light on the matter.

Thank you!

 

[Dadface]

I think the main difference is due to the difference in speed of the two waves.The longitudinal wave travels with a speed of root Youngs modulus/ density but the transverse waves travel much slower.For a string held in tension the speed of the transverse wave has a speed given by root tension* length/mass.I don't know the formula for the speed in a rod supported in the way shown in the link but apparently it is not independant of the diameter.If I find anything I will report back.
I had a quick search and it seems that the speed of the transverse waves is frequency dependant as well as diameter dependant..."high frequency transverse waves travel faster along a rod or bar than do low frequency waves".This makes things more complicated and I suspect it is the reason why the speed of transverse waves was not given in your link.

 

[sir-pinski]

Firstly, to answer your first question, the pattern of standing waves and the method of formula derivation will be different for a solid metal rod compared to a hollow tube. This is because the boundary conditions for the two are different. In a solid rod, the waves will bounce off the ends of the rod, while in a hollow tube, the waves will reflect off the open end and the closed end. This results in different patterns and formulas for the harmonics frequencies.

For your second question, striking the end of the rod in a transverse manner will not produce standing waves as the waves will not be able to reflect back and forth along the length of the rod. This is because the direction of motion of the waves will be perpendicular to the length of the rod, preventing them from bouncing back and forth. The formula provided in the link you shared is most likely for a different type of wave, such as a transverse wave, which is not the same as the longitudinal standing waves produced in a metal rod.

I hope this helps clarify any confusion you may have regarding standing waves in a metal rod. If you have any further questions, please don't hesitate to ask.