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Simple Beat Frequency Problem

  • #1

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



fbeat=f2-f1

f=nv/2L

v=[tex]\sqrt{}T/\mu[/tex]

The Attempt at a Solution



I used fbeat=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.
 

Answers and Replies

  • #2
1,860
0
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.
 
  • #3
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!
 
  • #4
1,860
0
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. :)
 
  • #5
120
0
if its so simple then do it yourself
 
  • #6
1,860
0
if its so simple then do it yourself
What are you talking about???
 

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