What is the mass of the string?

[timtng]

When the tension is 18 N, a string 2.00 m long has a fundamental frequency of 150 Hz.
a.) What is the mass of the string?
b.) With what tension must the string be stretched so that it vibrates in three segments at 150 Hz?

This is what I came up with:
a.) f=v/2L, v=2Lf=2*2*150=600 m/s
v=sqrt(T/μ), v^2=T/μ, μ=T/v^2=18/600^2=.00005 kg/m
M=2*.00005=.0001 kg

b.) L=3λ/2, 2=3λ/2, λ=4/3
v=fλ=150*4/3=200 m/s
v^2=T/μ, T=μ*v^2=.00005*200^2=2 N

Am I working both problems correctly?

Thanks

 

[Doc Al]

Your physics looks good. (I didn't check the arithmetic )

 

[M98Ranger]

for your response! Your calculations for both problems seem to be correct. In part a), you correctly used the equation for the speed of a wave (v) in terms of its frequency (f) and wavelength (λ) to solve for the linear density (μ) of the string. And in part b), you correctly used the equation for the speed of a wave (v) in terms of its tension (T) and linear density (μ) to solve for the tension needed for the string to vibrate in three segments at 150 Hz. Keep up the good work!