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JAMB Physics 2013 Paper

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Question : 22

Total: 43

What is the velocity of sound at 100 oC if the velocity of sound at 0 oC is 340ms -1?

497m^-1
440m^-1
397m^-1
240m^-1

Solution:

Concept:

The speed of sound in air is directly proportional to the square root of the absolute temperature.

Explanation:

Convert the temperatures to kelvin:

T_1 = 0^\circ\mathrm{C} = 273\,\mathrm{K}

T_2 = 100^\circ\mathrm{C} = 373\,\mathrm{K}

Using

V \propto \sqrt{T}

, we write:

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

Substitute

V_1 = 340\,\mathrm{m/s}

:

\frac{340}{\sqrt{273}} = \frac{V_2}{\sqrt{373}}

Solve for

V_2

:

V_2 = 340 \times \sqrt{\frac{373}{273}}

V_2 \approx 340 \times 1.169 \approx 397\,\mathrm{m/s}

Answer:

397\,\mathrm{m/s}

(Option C).

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