For a string fixed at both ends (length $L$): boundary condition requires nodes at both ends. $L = n\lambda/2 \Rightarrow \lambda_n = 2L/n$ and $f_n = nv/(2L) = (n/(2L))\sqrt{T/\mu}$. The fundamental ($n = 1$): $f_1 = v/(2L)$. Overtones: $f_2 = 2f_1$ (first overtone = second harmonic), $f_3 = 3f_1$, etc. All harmonics are present. Laws of vibrating strings: $f \propto 1/L$ (length), $f \propto \sqrt{T}$ (tension), $f \propto 1/\sqrt{\mu}$ (mass per length).