Hey Guys,

I see FREQUENCY has reared it head again. So, let me stir the pot a bit.

For several years, I have been asking (on other sites) the following question, "What can an angler do with the knowledge of the resonant frequency of a fly rod blank, other than to compare it with the value from another blank?" I have yet to recieve an answer.

Certainly, it can be useful for a blank manufacturer to use as a tool for quality control, as he knows the variables he can control to maintain consistency. But he doesn't really need the resonant frequency value, any precise method for measuring frequency will suffice.

I believe, for the angler, the resonant frequency value, in itself, is little more than an interesting number. This is because it has no predictive capabilities whatsoever. For that, one needs to know something about the K and m values of the rod and the harmonic oscillator formula. Believe me, you don't want to go there. (Been there, done that.) It's not worth it.

To put things in perspective, consider the resonant frequency of a new rod blank to be 195 cpm. By the time the builder attaches the necessary hardware (e.g., guides, etc,), the frequency of the rod itself is about 130 cpm. (This is a factor controlled to some extent by the builder.)

Now, before one can use it to fish, one must attach a line and a lure. (Just consider it weight.)

If the blank is to be used as a spinning rod, the amount of weight needed to to be added (i,e,, recommended lure weight) is that which will reduce the frequency of the "outfit" to about 105 cpm. Any more or less is a function of how the angler wants his "outfit" to "feel". That is, to adjust the frequency of his "outfit" to match his own PPF or Personal Preferred Frequency.

If the blank is to be used as a fly rod, the weight of line (ignore fly weight) required is that which will reduce the frequency of the outfit to about 83 cpm. Any more, and the rod will begin to feel like a bamboo rod (CCF=65 cpm.).

The moral of this story is, "The fundamental purpose of the flyline or lure weight is to adjust the frequency of one's "fishing outfit" to match one's PPF.

Nevertheless, frequency is the key in the relationship among rod strength (ERN), weight of line (ELN), and how one's fishing outfit "feels".
The "magic formula" is ERN - ELN = 5 Delta. For trout rods, a change of one ERN or ELN will change the frequency of one's outfit by about 5 cpm. It is up to each individual to determine what his own PPF is. Then he can adjust his outfit accordingly.

Or, if you attach a 10 gram weight (or 4 common cents) to the tip of your firmly fixed (at the butt) rod and tell me how many seconds it takes for 20 oscillations, I can tell you what line you should be using on that rod. Assuming you are a "normal" angler. I do not need to see your rod.

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Edited 1 time(s). Last edit at 04/08/2010 02:37PM by Bill Stevens.

Mr. Bill Steven,

I think this link would surfice your curiosity. [www.golfdiscussions.com]

Ben

Bill,
I think that you are right about the usefulness of resonant frequency to the average fisherman. But I think that being able to compare one blank to another is probably enough and very useful for most rod builders. And how much more can be done with it is determined by how well you understand it. It has been a very important tool for electrical and mechanical engineers and physicists for a couple hundred years. You said "one needs to know something about K and m values of the rod and the harmonic oscillator formula". I disagree with your over simplification. Knowing just the K (spring constant) and the m (mass) and the simple text book formula (one over two pie times the square root of the spring constant divided by the mass) is enough if you want to know the resonant frequency of a beam or a pipe or a simple spring and many other simple structures. However, a rod blank is a surprisingly complex structure, mainly because it has taper and varying wall thickness. Both the mass and the spring constant are more complicated than you suggest. But if we just look at the mass, knowing the mass density, the distribution of the mass, is necessary to calculate a blanks or rods resonant frequency. In fact, I think this is at the heart of why your Common Sense Frequency is not more useful to you and you do not believe, as virtually all engineers and physicists believe, that resonant frequency is an extremely important tool. When you add mass to the tip of the blank or rod you dramatically upset not just the mass but the mass density or how the mass is distributed
I will not argue with you about your PPF except to say it has very little to do with the actual resonant frequency. If you think that you can derive some indication of fly rod feel from it that is great but the relationship between your concept of PPF and resonant frequency is a tenuous one at best.



Edited 1 time(s). Last edit at 04/04/2010 01:13PM by Emory Harry.

Hey, it is just another tool! Tools are useful if used correctly. They can be dangerous if used incorrectly though:) As Emory states it is very important in electric and mechanical work.

Thinking it over.....rather than look at golf clubs perhaps we could consider "long canes" for the blind?

Emory, some of us do have O-scopes and would like to hear more about how you did the measuring. Some items that were once very costly for analog scopes can now be had quite cheaply on the used market. I'm certain I am way over thinking the process as I envision amplfiers, FFT plots and accelerometers....LOL!

Russ in Hollywood, FL.

Russell,
If you have a scope it is very easy. The most straight forward way is to mount a photo resistor in series with a second resistor and apply a small voltage, say 5 volts, across the two resistors. Then connect the input to your scope across the photo resistor and from a short distance away shine a light on the resistor while you deflect the rod tip and release it allowing it to oscillate back and forth through the light source. Each time it passes through the light source it will give you a pulse on the oscilloscope. It works better if the ligh source is well collumated but it does not something like a laser though I have used a laser and it works just fine. Also you may have to shield the photo resistor from the ambient room lights or you will get 60 cycles riding on top of the pulses.
If you have a digital scope or a storage scope that is a bonus as you can store the output of the photo resistor while the rod is oscillating and then take as long as you want to analyze the results. What model and make of oscilloscope do you have? There is a small chance that I was involved in its design.
If you have any trouble send me an e-mail and I will see if I can help.

Emory,

I'm pleased to see we are in disagreement, otherwise, this exchange would be boring. Now, let me respond to the comments you made in the previous thread, “Frequency and Blanks”.

Perhaps it is all semantics. ?

When I use the term "resonant frequency", I am speaking of the frequency of a freshly manufactured rod blank and only a freshly manufactured blank. Anything else, I simply consider to be a measure of the frequency of some specific sample. Otherwise, it seems to me, everything must be considered to have its own unique "resonant frequency" and the term becomes meaningless.

You stated, "I agree with your second paragraph that "all that is needed is a precise method of measuring resonant frequency".
Unfortunately, I did not say that . What I wrote was, "But he doesn't really need the resonant frequency value, any precise method for measuring frequency will suffice." Also, I did not suggest CCF was an answer.

I may well be wrong about resonant frequency being only an interesting number but not really useful. However, the source of that opinion is really irrelevant, as I am looking for someone to tell me of its relevance. Unfortunately, you offered nothing to make me change my opinion.

You say I am flat wrong and stated, "With careful use of resonant frequency a great deal can be predicted." OK, show me. I have a fly rod blank which has a resonant frequency of 192 cpm and another with a resonant frequency of 183. One is labeled 3wt and the other 6wt. Now, tell me, what can you predict about those two rods from the numbers 192 and 183? I don't believe you can even tell me which rod is which. Anyway, I believe the important number is the frequency of the the rod after the hardware has been attached. For that reason, I have concentrated my attention to what I call the angler’s “outfit”.

You stated, "... isn't it a little bit illogical for you to argue for CCF and argue that all that is needed is a precise method of measuring frequency and then make the statement that resonant frequency is useless??? "

I would answer, “Not necessarily”. First, I did not say the resonant frequency value was useless. It is a reasonable number for quality control if one wants one, however, I say it is essentially useless for rod builders. The resonant frequency of a rod blank represents the end point of the harmonic curve of frequency vs added weight, while the CCF treats the lower portion of that curve in the region of usefulness for rod builders.

Here, the curve is essentially linear. In your previous response to Tom, you stated: " I guess he achieved what he was trying to achieve but in my judgment what he achieved is not a measurement of frequency that can be used for any quantitative purposes." I would call your attention to my concept of Delta=5 cpm. I believe that is quantitative.

As for perspective, I will gladly admit my bias toward fly rods and fly rod "feel", but so what? That was my beginning, but it can all be extrapolated to casting rods of all types. After all, a rod is a rod is a rod.
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Now, for your recent comments.

You stated, “However, a rod blank is a surprisingly complex structure, mainly because it has taper and varying wall thickness. Both the mass and the spring constant are more complicated than you suggest. But if we just look at the mass, knowing the mass density, the distribution of the mass, is necessary to calculate a blanks or rods resonant frequency. ...”

What I get from that is you believe MOI (moment of inertia) measurements are very important in describing a rod and explaining its performance. I agree completely, however, I know MOI is too difficult to measure to be of any real use to the angler. I am a pragmatist, not a theoretical physicist. (Some day we will have to discuss my concept of MOIST, (MOI Substitute Term) which is the reciprocal of my X (expertise) Factor.)

You then went on, “... In fact, I think this is at the heart of why your Common Sense Frequency is not more useful to you and you do not believe, as virtually all engineers and physicists believe, that resonant frequency is an extremely important tool. ...”

I do not believe I said resonant frequency (the concept) was not an important tool. My point is that merely the knowing the resonant frequency of a rod blank is of little or no value to the common angler. I’m still waiting for someone to tell me what I can do with that number.

You then stated, “... When you add mass to the tip of the blank or rod you dramatically upset not just the mass but the mass density or how the mass is distributed.”

When one adds mass to the tip of a blank or rod to simulate the weight of a fly line or lure, one does nothing to the rod or blank, itself. Rather one creates a new system or “outfit”. Now, we have a new ball game—one in which I like to play and one which the average angler can comprehend and/or relate to.

Finally, you wrote. “ I will not argue with you about your PPF except to say it has very little to do with the actual resonant frequency.”

Finally, I can end the note on a point of agreement. I, also, don’t think PPF has much to do with “actual resonant frequency”. However, since my goal is not to promote resonant frequency, but rather to derive some concepts which might be useful for anglers, I am happy with it.
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Now, may I ask you a question?

In past months, I believe you have touted the idea that the sensitivity of a fishing rod was somehow directly related to the fundamental frequency of the rod. This would imply the stiffer the rod, the more sensitive it is.

However, there must be a tradeoff between stiffness and “pleasure derived from its use”. Therefore, it would appear a plot of fundamental frequency vs sensitivity vs pleasure must have an apex.

While it is a relatively simple matter to measure both the fundamental frequency and ERN of the rod, could suggest how and in what units one might plot data for “pleasure”? Or, is this something like PPF, a subjective concept?

Best wishes,
Bill

Bill,
I think that you are wrong about not being able to tell your two rod examples apart if you would allow me to look at them. I could tell a great deal about them. For example, just as a start the one with the lowest resonant frequency will be the one with the lowest stiffness if they are the same length or if they have simular stiffness the one with the lowest resonant frequency will be the longest.

Yes, sensitivity will increase as stiffness increases if the mass does not also increase. The variables that affect the resonant frequency and that affect the sensitivity are closely related in fact mostly the same variables but the variables are not as simple as the relationship that you keep referring to of just spring constant over the mass.
As far as attempting to measure something like "pleasure" is concerned you will not get me involved in that or the measurement of anything else that is inherently subjective.

You used the expression "harmonic curve of frequency vs added weight. I think that I know what you mean but I think that part of the difference of opinion between you and I is our use of terms. That is not an expression that in all of my years I have ever heard. A curve of the harmonics makes sense and a curve of frequency vs weight makes some sense but the two together makes no sense unless maybe you are talking about a three dimentional curve and I do not think that is the case. Resonant frequency is sometimes called the first harmonic or sometimes even called the natural frequency but "harmonic curve of frequency vs added weight????
A rod or blank oscillates at its resonant frequency when stimulated because the mechanical impedance drops dramatically at the resonant frequency. It also drops at each harmonic of that resonant frequency but not as sharply or as far. A harmonic is an integer multiple of the resonant frequency so you can see why your use of the word is not clear to me. By the way, you asked, I think somewhat skeptically about the relationship between resonant frequency and sensitivity. Not everyone realizes this but a vibration travels up the rod almost exclusively at the rods resonant frequency. The reason being that the mechanical impedance is much higher at other frequencies. The rod will normally convert Inputs at other frequencies to the rods resonant frequency because of the dramatic difference in impedance.

Thank you Emory. That is rather cheap and easy. I was thinking more along the line of impacting the blank and seeing what hertz it rang at. My scope is no tek, just a a lowly old hitachi V-1050f. Still I think it is up to the task at hand. I don't suppose you have bunch of 6dj8's from scope pulls you want to dispose of??

Bill, you ask about "pleasure derived from use". For me that is directly related to how many fish I put in the boat. Now I don't fly fish, don't catch bass, trout, or salmon and generally don't even cast. To make matters worse, most of my fish leave little doubt as to when they bite. It would appear my needs couldn't care less about the rod. I will concede that is somewhat true if I'm trolling and the rod is in a holder. Matters drastically change when I'm fishing light line for the class of fish. The ability of a blank to transmit info is key to how I fight the fish and when I can apply extra pressure. Then there is a quality which I am at a loss of words to explain. All I can say is some blanks have the ability to "store energy and latter use it to lift a fish". The ability to qualify and quantify the latter would be nice.

I suppose I should state I am in the minority and tend to fish lighter lines on stiffer rods than my peers.

Russ in Hollywood, FL.

Russell,
No, I am sorry I do not have any 6DJ8s around. It has been a lot of years since I used any of them. I will bet that you can find some though on one of the internet @#$%& sites.

You can somehow impact the scope and it will ring at the resonant frequency. The same frequency that it will oscillate at if you deflect it and release. As I mentioned previously it is very difficult to make a rod or blank oscillate at other than its resonant frequency. I would be a little careful how I impacted it though as it is fairly easy to damage a carbon fiber blank with impact.

The mechanical impedance curve looks just like the curve for a parallel resonant circuit. The impedance drops dramatically at resonance. And it has high Q just like many parallel resonant circuits. Adding weight tends to act like resistance in a parallel circuit and reduces the Q and also widens the Q so the blank will oscillate over a little range of frequenciews. A blanks spine tends to do the same thing.

All rods store energy. If they did not they would not work as fishing rods. When you apply force to the rod when casting or whatever and it deflects it is storing energy in the form of potential energy. Then when it is released it converts that stored potential energy mainly to kinetic energy and a little to heat energy as it moves or recovers.

(2) competitive blanks both rated at 9' 5 weight fast action.
Material of construction and weight are both claimed as competitive.
Upon test resonant frequency of one blank is higher than the other.
The assumption can be made that this blank has a center of mass closer to the butt which will make the tip feel lighter.
This, in turn, will make the rod lighter in hand to cast. The blank will dampen quicker and exhibit better accuracy due to the increased dampening.
Sensitivity will be improved and hook set will be quicker.
This should make for a more satisfying fishing experience.
The build for the blank with the higher frequency can be slowed down to match the build for the slower blank. The opposite can not be accomplished.

Eugene Moore

Dr. Bill,

You stated: My point is that merely the knowing the resonant frequency of a rod blank is of little or no value to the common angler. I’m still waiting for someone to tell me what I can do with that number.

Would it an advantage to cast further (distant wise) if you know the Resonant Frequency of one rod over the other and factor in the amount of weight you are casting ? Say in golf why do they select certain golf club for certain range ? Just curious.

Ben

Ben,

No, the Resonant Frequency of a rod blank has little if any relationship to the frequency of the rod built from it. Of course, it is always higher.

In theory, if one had two rods equal in everything except frequency, the rod with the higher frequency should enable one to cast farther. Unfortunately, all things are never equal so it probably would be that the rod which exhibited the frequency most nearly matchiny you PPF (Personal Preferred Frequency) would allow you to cast farther.

Golf clubs a chosen on the basis of the distance required, the loft of the club face, and a knowledge of one's personal swing characteristics.

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Eugene,

What you wrote is indeed true, if one could build a fishing tool using only a rod blank. Unfortunately the builder must apply hardware and this adds weight and reduces the frequency.

I believe the important factor is not the frequency of the blank, but rather, the frequency of the resulting fishing tool. How much the frequency is, or must be decreased, by the builder's action is really a function of what the builder wants the rod to "feel" like. This is a factor within his control.

Certainly, one can build a "minimalist rod" which will have a higher frequency than any other rod, but it does not follow that it will make for a "more satisfying fishing experience". Consider a Sage TCR 590 rod. While it is touted as a 5-wt rod, the average angler routinely fishes it using a No. 6 or 7 Line. I believe the reason for this is such a combination makes for a more satisfying fishing experience.

As for sensitivity being improved, that certainly sounds reasonable. However, let me play the devil’s advocate. I have never seen any quantitative data which supports the idea the magnitude of improvement is sufficient to be called “actual” rather than “psychological”. Of course, that would require a double blind test, a quantitative measure of sensitivity, and a plot of frequency vs sensitivity. I'm not holding my breath in anticipation of ever seeing such data.

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Emory,

You stated “I think that you are wrong about not being able to tell your two rod examples apart if you would allow me to look at them. I could tell a great deal about them.

I’m afraid you missed my point. I am certain you could tell a 3-wt rod from a 6-wt rod from a distance of 30 ft., if you were allowed to look at them. My question was, “what can you predict about those two rods from the numbers 192 and 183? My point being, resonant frequency numbers, by themselves, are essentially useless.
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You continued, “... As far as attempting to measure something like "pleasure" is concerned you will not get me involved in that or the measurement of anything else that is inherently subjective.

That is indeed unfortunate, as defining the “proper” fishing tackle is always a subjective matter. In the post above, Eugene relates it all to “a more satisfying fishing experience”. I believe that until one starts to consider subjectivity, one cannot really relate to anglers. Otherwise, you are just talking numbers.
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You stated, “ You used the expression "harmonic curve of frequency vs added weight. I think that I know what you mean but I think that part of the difference of opinion between you and I is our use of terms.

Please pardon my typos, I’m certain you understood I was referring to the harmonic oscillator curve, in which you appear to have little faith. I, on the other hand am quite impressed with the work of Grunde (Sexyloops) and the fit of fly rod performance to that curve.
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You closed with, “By the way, you asked, I think somewhat skeptically about the relationship between resonant frequency and sensitivity. Not everyone realizes this but a vibration travels up the rod almost exclusively at the rods resonant frequency. The reason being that the mechanical impedance is much higher at other frequencies. The rod will normally convert Inputs at other frequencies to the rods resonant frequency because of the dramatic difference in impedance.”

I am not really skeptical, but I am interested in the difference in elapsed time involved in transmitting a vibration through a rod with a resonant frequency of 100 cpm compared to one with a resonant frequency of 200 cpm. In other words, how much of a “jump start” (in fractions of a seconds) does the faster rod give the angler in setting the hook? Is it really something worth worrying about?

Best wishes,
Bill

For Emory, you have stated that the Resonant Frequency tells you everything about rod action, material, weight distribution, etcetera. Okay, I will bite! I have a rod with a resonant frequency of 140. From that number please tell me how long it is, what type graphite it is made from and what the action is.

Obviously I am making a point. I agree with Dr. Hanneman the resonant frequency numbers by themselves are useless. This is also the case with almost any other type measurement number you come across though. In an earlier thread on this subject somebody mentioned that the numbers did not have any meaning until you had more than one in order to make a comparison. I see the value in that, but not in a number by itself. I do not think you can tell much about a rod from a resonant frequency number all by itself.

Dr. Bill,

I am interested on how you define and measures Resonance Frequency. Also is your term "Frequency" = CCS (Action Angle) ?

Ben

Bill,
If you have a friend on another site, Sexy Loops, that has invented the term "harmonic curve of frequency vs added weight" that is fine and I hope it is something that is useful to you. But do not expect me to understand what your friend means by these words. That is a term that in my experience engineers do not use.

Your last paragraph suggests to me a lack of understanding on your part. Resonant frequency and the velocity that a vibration will travel up a rod are two different things. If your two sample rods are constructed of the same material then there will be almost no difference in velocity of the vibrations for the two rods with two different resonant frequencies. And as far as giving the fisherman a jump start in setting the hook is concerned, I almost do not know how to respond to that. Vibrations travel through air at sea level at roughly 1,000 feet per second but through a carbon fiber rod they travel at roughly 10 times that speed or 10,000 feet per second! From the fisherman's standpoint it is for all practical purposes instantaneous.

You are in error in your response to Eugene. Sensitivity can be measured and it can be very significant from one rod to another. That is sensitivity of the rod not of the fisherman's hand. I can measure how much of the input energy at the tip of the rod gets to the fisherman's hand and I call that the rods sensitivity. Now what that does to the fisherman's "fishing experience" or his "Personal Preference Frequency" I will leave that up to you.

You are also in error with in your response to Ben about resonant frequency and casting distance. The resonant frequency will determine the rods tip velocity or how rapidly the rod can release in the second part of a cast the eneregy that is stored up in it in the first part of the cast. This in large measure determines casting distance or how much input is required to cast any given distance.

At this point I would like to bow out of this discussion. I think that if you insist on using subjective terms like Personal Preferance Frequency and I insist on using more quantifiable, measurerable terms there is not going to be any meeting of the minds.

I do have a final question for you though. You started off by coming up with what I think were very useful, measureable, quantifiable terms for a rods action and power. They were not new terms but you came up with a practical way of measuring them, quantifying them. Where did you start down this path to meaningless, subjective terms like Personal Preference Frequency?

Ben, I think this is more what Dr. Hanneman is referring to..... [www.common-cents.info]

Peter,
I would agree with you that the number for resonant frequency in isolation or by itself does not tell you very much and is not very usefull. I would suggest that no single characteristic of the rod in isolation is very useful. If all you know about a rod is its weight that does not tell you enough or if all you know is the action angle that is not enough to be useful. However, you do not need much more information before it starts to mean more and the more additional information you have about the rod the more meaningful or informative the resonant frequency becomes. For example, if I just get a good look at the rod from its appearnace and the knowledge of its resonant frequency I can tell quite a bit. If I could also pick it up so as to get a rough indication of its weight that in combination with the resonant frequency tells me even more. If I could measure its stiffness and its action that information in combination with the resonant frequency really tells me a great deal about the rod.
To answer a little differently, I believe, and others who have taken a very scientific approach to quantifying rods properties, believe that a rods resonant frequency is the single most important characteristic but I do agree with you that by itself it does not tell us enough.



Edited 1 time(s). Last edit at 04/05/2010 03:26PM by Emory Harry.

I have not measured but I want to be clear. I hear numbers in the range of 100-200 CPM for raw blanks. So we are saying 1.67 to 3.33 hertz, correct? That is slower than I would have imagined.

There is a fair body of work that has been done with regards to sensitivity of the human hand with various shaped tools made of different materials. I suggested looking at long canes for the blind. One can even look at human nerve limitations.

Work with long canes has shown a somewhat linear performance increase from various materials such as fiberglass to aluminum but more of a quadratic leap with graphite. Light and stiff are of prime importance. Some of us are old enough to have fished with metallic rods and certainly fiberglass and graphite. I don't think anyone is doubting the superior performance of graphite nor the light and stiff part.

IIRC the hand is most sensitive around 250 hertz and the middle finger has the most feeling. Look at it this way, can you both hear and feel braid singing through your guides on a harding running fish? Now we know we can't hear a few hertz. Truth is our hand can't really feel it either. IIRC the range is something around 8-500 hertz. Therefore it should be clear that vibrations don't travel up the rod at its resonant frequency.

It is also known that some "sensors" are directly related to muscle action and some are not. The good news is we respond to impluses more strongly and I'd consider a fish nibble an impluse. It makes me wonder if we couldn't tailor the rod to best produce the ranges we feel the most.


Now be nice to me guys. This stuff is way out of my field and I'm going by memory. It is also possible you guys are primarily concerned with casting performance.

Russ in Hollywood, FL.

Russell,
I think that you are right that is a little on the low side for resonant frequency. It is in the range of what fly rods resonate at but as a rod gets stiffer it will increase, as it get shorter it will increase and as the mass is reduced it will increase so some rods can be an order of magnitude higher than the numbers you used.
I did not know the range of frequencies that your hand was most sensitive to, that is interesting. But if I read what you said correctly the resonant frequency of most rods will be within the range that you pointed out. Plus I suspect that what we can feel is like what we can hear and is amplitude sensitive. The higher the amplitude the wider the range of frequencies that we can hear. How our hearing is a function of amplitude is very interesting if you are interested in Hi-Fi. Look up on the Internet "Fletcher Munson Loudness Contours" and you will find it very interesting. But the point is that what your are hearing when line is drawn across a guide is a different vibration and is coming to you mainly through the air if you are hearing it not through the rod.
The frequency of pulls or releases of tension or yanks on the line can obviously be felt and I think that you have better described these as impulses. But the rod will try to convert these impulses to a frequency and transmit it up the rod at the rods resonant frequency. When you deflect a rod and then release it you have introduced an impulse but look what the rod does to it. When the rod is released the rod oscillates at its resonant frequency and then damps out the oscillations but as the amplitude of the oscillations damp out the frequency remains the same, the rods resonant frequency. Look at impedance curve of a parallel electrical resonant circuit on the Internet. That is exactly what the curve of impedance for a rod looks like. You can see that the impedance or resistance to transmitting a vibration at any other frequency other than the resonant frequency is very high.
There is a math tool that you might also want to look up if you are REALLY interested called a Fourier Transform that shows how an impulse is converted to a frequency or a frequency to an impulse.

Your next to last paragraph about tailoring the response of a rod to match the frequency sensitivity of the hand is interesting and I think it deserves some more thought.



Edited 1 time(s). Last edit at 04/05/2010 07:23PM by Emory Harry.