Finding the possible frequencies of a tuning fork

[chris097]

Homework Statement

A 0.0120 kg, 2.05 m long wire is fixed at both ends and vibrates in its simplest mode under a tension of 202 N. When a tuning fork is placed near the wire, a beat frequency of 5.10 Hz is heard. What are the possible frequencies of the tuning fork? (enter the smaller frequency first) (It asks for 2 answers)

Homework Equations

f = √(TL/m)/2L
f_b = |f₁ - f₂|

The Attempt at a Solution

I first found the frequency of the string using equation 1 then I simply thought that the frequency of the tuning fork would always be multiples of 5.10 Hz from the frequency of the fork. So i got answers like 50.4, 50.5...


Can anyone please help out?
Thanks!

 

[willem2]

Just use the second equation you listed in section 2. you know $f_b$ and $f_1$ so what can $f_2$ be?

 

[chris097]

Just use the second equation you listed in section 2. you know $f_b$ and $f_1$ so what can $f_2$ be?

I end up getting 50.4 and 55.5 Hz, which is wrong.

 

[Delphi51]

f - 5.1 and f + 5.1