Does Tension Affect Frequency and Velocity in Wave Equations?

[jvdamdshdt]

Homework Statement

Hello guys I am having problems with wave and frequency problems. I know the equation use to find frequency are ∫=λ/v and
∫=1/2L(\sqrt{FT/μ})

So my question is: if the length and μ are kept the same will FT be directly proportional? Will frequency increase as the tension increase?

*v=\sqrt{FT}
I have the same question about velocity when the μ is kept constant.

Homework Equations

v=\sqrt{FT}
∫=1/2L(\sqrt{FT/μ})

The Attempt at a Solution

I said when the velocity increases as the tension increases. I know that numbers in the numerator are directly proportional to what you are trying to find but the square root is throwing me off.

 

[mfb]

Please specify the physics problem you are considering - I guess waves on a string with mass density µ.

So my question is: if the length and μ are kept the same will FT be directly proportional?

It does not make sense to ask "is [variable] proportional"? "Proportional" is a relation between two variables. The frequency and tension are not proportional to each other due to the square root - just plug in numbers to verify that.

$v=\sqrt{F_T}$

That is not right.

I said when the velocity increases as the tension increases.

Right.

 

[jvdamdshdt]

Please specify the physics problem you are considering - I guess waves on a string with mass density µ.

It does not make sense to ask "is [variable] proportional"? "Proportional" is a relation between two variables. The frequency and tension are not proportional to each other due to the square root - just plug in numbers to verify that.
That is not right.

Right.

Thank you for the reply. I am having problems with the equations and general common sense question. Let's say an object on a string experiences Simple Harmonic Motion. The strings have the same linear densities and lengths. String one has FT while string two has 2FT. What can be said about their frequencies?

From the equation ∫=1/2L (\sqrt{FT/μ})

By removing the constants I am left with f=\sqrt{FT}
Q: By increasing the string by 2FT will the frequency increase by 2?

 

[mfb]

By removing the constants I am left with f=\sqrt{FT}

No, you get f=c\sqrt{F_T} with some constant c.
20=5*4 does not imply 20=4 just because 5 is constant!

Alternatively, you can write f \propto \sqrt{F_T} ("f is proportional to the square root of F_T").

Q: By increasing the string by 2FT will the frequency increase by 2?

Did you plug in some numbers?
F_T=1N, F_T=2N, use any µ you like. Which frequencies do you get?