Find New Frequency When Length AND Diameter Is Decreased?

[justinh8]

Homework Statement

Hi, i need some help with this question,
A string of length 60cm and diameter 0.80 mm is under tension 64 N. When plucked, it emits a frequency of 660Hz. What is the new frequency if the length is decreased to 40cm, the diameter decreased to 0.50mm and the tension increased to 100 N? Please explain, Thanks!

Homework Equations

f1/f2 = L2/L1, f1/f2 = Square Root F1/ Square Root F2, f1/f2 = d2/d1

The Attempt at a Solution

I can do it when one of the variables are decreased but i have no idea where to start when 3 variables are changing.

 

[Simon Bridge]

The wave speed depends on the tension, the wavelength depends on the length of the string. Do each separately and combine to get frequency. The equation you are missing is v=fλ.