Standing waves and banjo string

[phyzeek]

1. A banjo string 36.0 cm long oscillates in a standing wave pattern. It resonates in its
fundamental mode at a frequency of 250 Hz. What is the tension in the string if 80.0 cm of the
string has a mass of 0.75 grams?

Homework Equations

k=2pi/lamda
velocity=sqrt(F_tension/miu)
miu=m/l
w=2pif

The Attempt at a Solution

v=sqrt(F_t/miu)
solved for miu and plugged into equation: 7.5*10^-4/.8
v=lamdaf
L=lamda/2
--> v=2Lf
v=2(.8)(250)
then equated both equations

i think i got confused with which length to use

 

[grzz]

I think your work is ok.

Yes - mu =m/L and for fundamental frequency lambda = 2L.

 

[phyzeek]

I'm not sure when to use the length of the banjo string (36cm) :[

 

[grzz]

When the string is vibrating in its first overtone, i.e. its second harmonic, then the length of string will be the wavelength.

 

[phyzeek]

thank u. my answer is still incorrect... i would appreciate any more help. thank you

 

[grzz]

I think your work is ok.

Yes - mu =m/L and for fundamental frequency lambda = 2L.

May I correct my own contribution above.

mu = m/L where L = 0.80m but lambda = 2 x 0.36 since this is the length which is oscillating.