Calculating Frequency Changes in a Guitar String

[Shaley]

A guitar string 60 cm in length, with a diameter of 1.4 mm and a tension of 289 N, emits a note with a frequence of 147 Hz. Find the frequency in each of the followig situations:

a)the tension isreduced to 196N
b)a string of the same material, 45 cm long and 1mm in diameter under 168 N of tension, is plucked.

I have no idea for a, but I was hoping someone could check my work on b?
=Fi(square root of tension fraction)(length fraction)(diameter fraction)
=147Hz(square root of 169/289)(60/45)(1.4/1)
=209.8Hz

I am just getting confused as to if the 289 goes on top of the fraction, or the 169.

thanks for your help in advance!

 

[mgb_phys]

It would help if you put units in the equations then you can easily check that you have them the correct way around.

frequency = sqrt ( Tension / mass per unit length )
s^-1 = sqrt ( N / Kg m ^-1 )
s^-1 = sqrt ( kg m s^-2 / Kg m ^-1 ) = sqrt(s^-2)

 

[Shaley]

thankyou. Can you please help me with part a as well?

 

[mgb_phys]

The frequency is proprtional to sqrt(tension)

 

[Shaley]

thanks again