Relationship Graph Between Frequency and Tension

In summary: If not, it would be interesting to see what the y-intercept would be.Yes, the curve does go through the origin.
  • #1
Stormblessed
24
2

Homework Statement



After plotting a graph with frequency (f) of a wire on the y-axis and tension (C-Clamps) on the x-axis, a root curve was obtained. If the trend of the line is maintained, does it pass through the origin? Should it?

Note: graph attached

Homework Equations



f is proportional to square root of T

The Attempt at a Solution



I said that the curve would not pass through the origin if the line was hypothetically extended, as the wire can still vibrate at a specific frequency without any tension. Therefore, the y-intercept of the curve would represent the natural frequency of the wire.

I still feel like this response is wrong, however, because when I plotted a graph of f^2 vs T, the resulting line passed through the origin. But based on the f vs T graph, it doesn't look like it would pass through the origin. I also do not know for sure if the y-intercept of the curve represents the natural frequency of the wire and if the line should pass through the origin.
 

Attachments

  • f vs T graph.pdf
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  • #2
If the tension is zero, then where is the restoring force, when you pull on the string?
 
  • #6
Sorry, my phone went a little haywire multiple posts.
 
  • #7
scottdave said:
If the tension is zero, then where is the restoring force, when you pull on the string?

Is the restoring force zero since
scottdave said:
Sorry, my phone went a little haywire multiple posts.


Is the restoring force zero, since tension is zero? How would that relate to the curve going through the origin or not?
 
  • #8
if tension zero, wire cannot vibrate.
I know this experimentally because I can play guitar-like instruments and bowed instruments! :)
natural frequency of a wire is undefined.
 
  • #9
musician ilhan said:
if tension zero, wire cannot vibrate.
I know this experimentally because I can play guitar-like instruments and bowed instruments! :)
natural frequency of a wire is undefined.

So that means the curve does pass through the origin then?
 
  • #10
scottdave said:
If the tension is zero, then where is the restoring force, when you pull on the string?

I'm assuming that it will go through the origin, as the wire cannot vibrate without tension
 
  • #11
Stormblessed said:
I'm assuming that it will go through the origin, as the wire cannot vibrate without tension
Yes, you are correct. It is hard to tell if your square root curve will extrapolate and hit the origin.
 

Related to Relationship Graph Between Frequency and Tension

1. What is the relationship between frequency and tension?

The relationship between frequency and tension is inverse. This means that as frequency increases, tension decreases and vice versa. This is known as Hooke's Law, which states that the force applied to a spring is directly proportional to its extension.

2. How does tension affect frequency?

Tension directly affects the frequency of a vibrating object. As tension increases, the frequency also increases. This is because a higher tension means a higher restoring force, which leads to a faster vibration and thus a higher frequency.

3. What factors can affect the relationship between frequency and tension?

The relationship between frequency and tension can be affected by the material of the object, the length or size of the object, and the amount of force applied. Other factors such as temperature and air resistance can also have an impact on this relationship.

4. What is resonance and how does it relate to frequency and tension?

Resonance occurs when an object's natural frequency matches the frequency of an external force or vibration. In terms of frequency and tension, resonance can occur when the tension is adjusted to match the natural frequency of the object, resulting in a higher amplitude and louder sound.

5. Can the relationship between frequency and tension be applied to other systems besides springs?

Yes, the relationship between frequency and tension can be applied to other systems such as guitar strings, piano strings, and even the vocal cords. In these systems, the tension of the string or vocal cords can be adjusted to produce different frequencies and pitches.

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