Frequencies of the first three overtones in a string?

[Tom Beckham]

Homework Statement

A violin has an A string in tune at 440.0 Hz; as is the E string at 660.0 Hz. The tension force on each of the strings is 25.0 N. The linear density of the A string is 1.00 g/m. What are the frequency of the first three overtones for each string?

Homework Equations

f = v/ λ
λ = 2L/n
v = √(T/P)

f = frequency
λ = wavelength
v = velocity of wave
L = string length
T = tension
P = Linear Density in kg/m
n = number of loops

The Attempt at a Solution

String A:

f = (n√(T/P))/2L
L = 0.17967748671

f = (2√(T/P))/2L for the 1st overtone
f = (3√(T/P))/2L for the 2nd overtone
f = (4√(T/P))/2L for the 3rd overtone

Is this path right?

 

[PietKuip]

Do this without a calculator.

 

[Tom Beckham]

Do this without a calculator.

Oh yeah, thanks!