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JAMB Physics 2010 Paper

Question : 39

Total: 47

Solution:

Concept:

Speed of sound in a gas is independent of pressure and depends only on the absolute temperature.

Explanation:

The relation is

V \propto \sqrt{T}

Using two states,

\frac{V_1}{\sqrt{T_1}} = \frac{V_2}{\sqrt{T_2}}

Convert temperatures to kelvin:

T_1 = 16 + 273 = 289\ \mathrm{K}

and

T_2 = 127 + 273 = 400\ \mathrm{K}

Given

V_1 = 340\ \mathrm{m\,s^{-1}}

Substitute values:

V_2 = V_1 \sqrt{\frac{T_2}{T_1}} = 340 \sqrt{\frac{400}{289}}

Since

\sqrt{\frac{400}{289}} = \frac{20}{17}

, we have

V_2 = 340 \times \frac{20}{17} = 400\ \mathrm{m\,s^{-1}}

Doubling pressure has no effect on the speed of sound at a fixed temperature.

Answer:

400\ \mathrm{m\,s^{-1}}

(Option A).

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