The speed of sound in oxygen at S.T.P. will be approximately: (Given, $$R = 8.3$$ J K$$^{-1}$$, $$\gamma = 1.4$$)

We need to find the speed of sound in oxygen at STP.

The values of the gas constant and the adiabatic index are given as $$R = 8.3$$ J/(mol K) and $$\gamma = 1.4$$, respectively, while at STP the temperature is $$T = 273$$ K and the molar mass of $$O_2$$ is 32 g/mol = 0.032 kg/mol.

The speed of sound in a gas is given by the formula $$v = \sqrt{\frac{\gamma RT}{M}}$$.

Substituting in the numbers leads to $$v = \sqrt{\frac{1.4 \times 8.3 \times 273}{0.032}}$$.

Since the numerator is $$1.4 \times 8.3 = 11.62$$, multiplying this by 273 gives $$11.62 \times 273 = 3172.26$$.

This gives $$v = \sqrt{\frac{3172.26}{0.032}} = \sqrt{99133} \approx 315 \text{ m/s} \approx 310 \text{ m/s}$$.

Therefore the correct answer is Option 1: 310 m/s.