Seemingly simple Physics 2 wave question (third harmonic frequency)

[novera]

Homework Statement

A string vibrates at its third-harmonic frequency. The amplitude at a point 35 cm from one end is half the maximum amplitude. How long is the string?

Relevant Equations

y=Acos(ωt)sin(kx)

I cannot find the correct answer anywhere online and the answer I keep getting is 5.4 (incorrect)

Please show me the process to get to the answer! Thank you

 

[RPinPA]

1. For what values of the argument ##\theta## does ##\sin(\theta)## equal 1/2? 35 cm corresponds to ##kx## having that value. Since you know what ##x## is, that gives you possible values for ##k = 2\pi/\lambda## and therefore you can work out ##\lambda##.

2. For the third harmonic, what is the relationship between ##\lambda## and the length of the string?

3. If you want a comment on your calculations, show your calculations. Saying "I got 5.4" is pointless and carries no information. Also you didn't include any units. Was that 5.4 km? mm? miles? Light years?

It seems to me that as there are multiple answers for my first question, there are multiple answers to this problem.