Relationship Graph Between Frequency and Tension

[Stormblessed]

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.

 

[scottdave]

If the tension is zero, then where is the restoring force, when you pull on the string?

 

[scottdave]

You may find this helpful in explaining why T^2 appears to point toward origin.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html

 

[scottdave]

You may find this helpful in explaining why T^2 appears to point toward origin.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html

 

[scottdave]

You may find this helpful in explaining why T^2 appears to point toward origin.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/string.html

 

[scottdave]

Sorry, my phone went a little haywire multiple posts.

 

[Stormblessed]

If the tension is zero, then where is the restoring force, when you pull on the string?

Is the restoring force zero since

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?

 

[musician ilhan]

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.

 

[Stormblessed]

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?

 

[Stormblessed]

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

 

[scottdave]

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.