A violin string resonates at its fundamental frequency of 196  Hz. Where along the string must you place your finger so its fundamental becomes 440  Hz ? For the fundamental, L=(1)/(2) λ. Since λ=v / f, it follows that f1=v / 2 L. Originally, the string of length L1 resonated at a frequency of 196  Hz, and therefore 196  Hz=(v)/(2 L1) with a resonance at 440  Hz, 440  Hz=(v)/(2 L2) Eliminate v from these two simultaneous equations and find (L2)/(L1)=(196  Hz)/(440  Hz)=0.445 To obtain the desire
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