Calculating Fractional Increase in Tension for Beat Frequency Problem

[UnPhysStudent]

Homework Statement

Two identical piano wires have a fundamental frequency of 600 Hz when kept under the same tension.What fractional increase in the tension of wire will lead to the occurrence of 6.0 beat/sec when both wires oscillate simultaneously?

Homework Equations

f_beat=f₂-f₁

f=nv/2L

v=\sqrt{}T/\mu

The Attempt at a Solution

I used f_beat=f₂-f₁ to solve for f₂ and ended up with 606Hz. I am really confused as to how to proceed. We were told that the answer should be 0.02 but I have know idea how to get that. Can you please give me a hint as to how to begin?

Thank you.

 

[Mindscrape]

You can also find the ratio of the tensions (that's what it means by fractional increase)

T=µv^2=µ*(2Lf/n)^2

so then look at T2/T1.

 

[UnPhysStudent]

You can also find the ratio of the tensions (that's what it means by fractional increase)

T=µv^2=µ*(2Lf/n)^2

so then look at T2/T1.

I tried doing that and at first I ended up with 1.02. After staring at it a little I released that I needed to subtract 1 from my answer to get the fractional increase.

Thanks so much for your help!

 

[Mindscrape]

Well, the ratio between them is 1.02 like you said, so T2 is 1.02 times greater than T1, or in percentages 102%. Fractional increase and percent increase is how much over 1 or 100%, respectively, the numbers are. If someone says a shirt increases in price by 250% then the shirt is really 350% of what it used to be, NewPrice=3.5*OldPrice. I personally don't see why people don't just say the shirt is 350% what it used to be, or has increased to 350% of the old price, but I'm not the one making the rules. :)

 

[Luongo]

if its so simple then do it yourself

 

[Mindscrape]

if its so simple then do it yourself

What are you talking about?