The term "local speed of sound" is used because the speed of sound's propagation through the air is a function of the velocity of the air molecules themselves. Since the Temp of the air reflects this average molecular velocity, the LSS is a function of air Temp (not altitude). The formula to find the LSS (in kt) is 39xsqrt(T), where T is the Temp expressed in Kelvin (Celsius + 273). Hence @ the standard SL Temp of 15°C the LSS is approx 662kt.
MF