posted by Anonymous .
a wire under tension vibrates with a fundamental frequency of 256Hz. what would be the fundamental frequency if the wire were half as long, twice as thick, and under 1/4 tension?
The speed of transverse waves is the squareroot of (T/p), where p is the density per unit length, and T is the tension foorce. The density per unit length is 4x higher for the shorter, fatter wire, and T is 1/4 as high, to the sound speed is 1/4 as large.
The wavelength of the fundamental is 1/2 as long due to the shorter length.
The fundamental frequency scales with (sound speed)/(wavelength), and gets multiplied by (1/4)/(1/2) = 1/2