## Physics: Principles with Applications (7th Edition)

The maximum length L of a piano string (and hence the maximum wavelength of the fundamental frequency) is constrained by the size of the piano. For a fixed string length L and wavelength $\lambda$, in order to play a low note, i.e., minimize the frequency f, we must minimize the wave speed v, because $v = \lambda f$. The speed of a wave on a string is given by equation 11-13, $v = \sqrt{\frac{Tension}{linear mass density}}$. To achieve this goal of minimizing v and lowering the string’s fundamental frequency, we want the string’s linear mass density (i.e., mass per unit length) to be large. Accordingly, bass strings on a piano are often steel wires, wrapped with a coil of copper or lead.