Halliday, Resnick & Walker — Waves–II: Problem 108

Chalk squealing on a chalkboard. To make a chalk stick squeal when drawn across a ceramic (clay) chalkboard (Fig. 17.30), first rub it several times over the area to be used. Then hold the chalk stick about 30° from a perpendicular to the board and pull it. The chalk can undergo repeated stick and slip, producing the irritating squeal. The oscillations responsible for the sound occur in a shear layer that is a 0.3-mm-thick layer between the board and chalk stick whenever the chalk slips after sticking. Waves from that oscillating layer travel into the board, which radiates the sound much like a drumhead. If the frequency of the squealing is 2050 Hz, what is the wavelength of the sound that reaches you? (If the chalk stick is short, your grip on it damps out the oscillations, eliminating the squeal.)