Athin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. it is vibrating in its third overtone, and the equation for the vertical displacement of any point on the string is y(x, t) = (1.22 cm) sin[(14.4 m-1)x] cos[(166 rad/s)t]. (a) what are the frequency and wavelength of the fundamental mode of this string? (b) how long is the string? (c) how fast do waves travel on this string?

Asheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200oc and is permitted to achieve a steady-state diffusion condition. the diffusion coefficient for nitrogen in steel at this temperature is 6 x 10- 11 m2 /s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 -s. also, it is known that the concentration of nitrogen in the steel at the high-pressure surface is 4 kg/m3 . how far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3 ? assume a linear concentration profile.