Ring Impedance & String Connection: Is It Valid?

In summary: So if you want to calculate the motion using a different equation, you'll need to convert the speed v into a suitable dimensionless quantity.
  • #1
gasgas
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Homework Statement
Suppose there are two strings with equal tension but different impedances attached to a ring on a vertical rod. If we shake the first string, it will make the ring slide and transmit the wave to the other string. As the ring slides on the rod, there is friction acting on it which is equal to F=b*v where b is coefficient of friction and v the speed of the ring. What is the value of b if there is no wave reflection?
Relevant Equations
F=Z*V
R=(Z1-Z2)/(Z1+Z2)
If we consider the coefficient b as the rings impedance, we can consider the effective impedance on the right to be b+Z2 where Z2 is the impedance of the second string. Then because there is no reflection it follows that Z1=b+Z2 or b=Z1-Z2.
Is this a valid solution? My professor went through a more complicated derivation which we concluded was wrong so I tried this. Is it correct? Can we suppose that the ring and string are connected in series and can we equate b with impedance? They match dimensionally so i don't see why not. Any help appreciated :)
 
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  • #2
My doubt would be whether there may be a constant multiplier needed to convert b to a comparable impedance. I see no way other than to analyse the motion fully.
 
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  • #3
I agree with @haruspex that this is a complicated problem, and I'd be inclined to analyze it fully from a motion and wave equation standpoint, instead of trying to simplify it to the impedance/reflection equation. Perhaps there is a simpler way to do it, but I'm not seeing it intuitively.

Also, it doesn't look like it's specified in the problem statement, but it seems clear to me that this can only work if the impedance of the 2nd string is lower than the first. The friction at the ring would seem to add impedance, so if the 2nd string had higher impedance than the first, I don't think there is any way to avoid reflections at the ring junction.

I also don't understand this part of the problem statement, about the frictional force depending on the velocity. That's not normally how frictional forces work, but maybe it helps with the math somehow...
gasgas said:
As the ring slides on the rod, there is friction acting on it which is equal to F=b*v where b is coefficient of friction and v the speed of the ring.
 
  • #4
berkeman said:
maybe it helps with the math somehow.
It will. With b negative, it arranges that the frictional force always opposes the motion.
 
  • #5
But speed dependent?
 
  • #6
berkeman said:
But speed dependent?
That's the price of making the math more manageable.
Bear in mind that standard damped oscillation analysis assumes F∝v.
 
  • Informative
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1. What is ring impedance and how does it affect string connection?

Ring impedance refers to the resistance or opposition to the flow of electrical current in a closed circuit. In the context of string connection, it refers to the amount of resistance encountered by the electrical signal as it travels through the string connection. This can impact the overall performance and reliability of the connection.

2. How is ring impedance measured?

Ring impedance is typically measured in ohms (Ω) and can be calculated using Ohm's Law, which states that resistance is equal to voltage divided by current. It can also be measured using specialized equipment, such as a network analyzer.

3. What factors can affect ring impedance in a string connection?

There are several factors that can affect ring impedance in a string connection, including the type and length of the string, the type of connector used, the quality of the connection, and the materials used in the connection. Other factors such as temperature and humidity can also have an impact.

4. Why is it important to consider ring impedance in string connection?

Ring impedance can have a significant impact on the performance and reliability of a string connection. If the impedance is too high, it can cause signal loss or interference, leading to poor performance or even connection failure. By considering ring impedance, engineers can ensure that the connection is optimized for maximum performance and reliability.

5. Is it valid to use a ring connection in all types of string connections?

While ring connections can be used in many types of string connections, it may not be the most suitable option for all situations. Factors such as the type of string and the intended use of the connection should be taken into consideration when deciding on the best type of connection. It is important to consult with a qualified engineer to determine the most appropriate connection for a specific application.

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