The speed of sound in gold at room temperature is about 3200 m/s, and the distance between neighboring atoms in the lattice is about 4 1010 m. The...

The speed of sound in gold at room temperature is about 3200 m/s, and the distance between neighboring atoms in the lattice is about 4 × 10−10 m. The mass of a gold atom is 3.3 × 10−25 kg. (a) Compute the effective spring constant of the interatomic interactions. (b) A sound wave of frequency 440 Hz (A4, the A above middle C) is propagating through gold. Find the period T, wavenumber p, and wavelength λ of this wave. (c) Comment, in a couple of sentences, on whether a linear dispersion relation between ω and k is a good approximation for this wave.