Guitar String and frequencies?

[gmmstr827]

Homework Statement

A guitar string is 90.0 cm long and has a mass of 3.16 g. From the bridge to the support post is 60.0 cm and the string is under a tension of 520 N. What are the frequencies of the fundamental and first two overtones?

L_s = 90.0 cm = .9 m
L_bsp = 60.0 cm = .6 m
m = 3.16 g = .00316 kg
F_t = 520 N

Homework Equations

v = sqrt(F_t*L_s/m)
v = λf >>> λ = v/f
λ = 2L_bsp/n; n = 1 for fundamental, n = 2 for 2nd harmony, etc.

The Attempt at a Solution

Find the velocity:
v = sqrt(TL_s/m)
v = sqrt[(520 N)(0.900 m)/(3.16e-3 kg)]
v = 384.8 m/s

Fundamental:
Set λ = v/f and λ = 2(L_bsp)/n equal to each other, n = 1, plug in other variables, solve for f.
(384.8 m/s)/f = 2(0.600 m)/1
384.8 m/s = (1.200 m)f
f = 320.7 Hz for the fundamental

Second harmonic:
Repeat same steps as the fundamental, but with n = 2.
(384.8 m/s)/f = 2(0.600 m)/2
384.8 m/s = (0.600 m)f
f = 641.3 Hz for the second harmonic.

Third harmonic:
Repeat the same steps as the fundamental and second harmonic, but with n = 3.
(384.8 m/s)/f = 2(0.600 m)/3
384.8 m/s = (2(0.600 m)/3)f
f = 962.0 Hz for the third harmonic.^^^ Does this all look correct?

 

[anathema]

Yes, your calculations and methodology are correct. Your final answers for the fundamental and first two overtones are also correct. Great job!