A study of the monthly wind speed v near the ground surface and the power law index for 22 stations in India and Bangladesh has led to relations of the form alpha = Ae(-bnu) for each of the stations, where A and b are station dependent. A collective fit for the equation for three stations in the coastal plains is alpha = 0.43e(-0.19nu), and for three stations in the inland plains, it is alpha = 0.71e(-0.34nu). These correlations have been found to give estimates of the monthly alpha for different stations in the plain lands with the rms error of 0.05. The same fits are found to predict the annual alpha from the annual average of wind speed with rms error of 0.025, while the annual alpha ranges between 0.14 and 0.54. For the correlations computed, the alpha values for nu around 5 or 6 m/s agree with the figure 0.14 of the 1/7 power law, but for lower speeds, these differ strongly. Therefore, the 1/7 power law may be considered as a special case of the exponential relations for high surface wind speeds. The collective fits show that the wind speed gets remarkably larger with height for low surface winds. Hence, for locations having low winds, large hub heights are recommended for wind machines.