For accurate tuning of a musical instrument the speed of sound in hydrogen has to…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

For accurate tuning of a musical instrument the speed of sound in hydrogen has to match the speed of sound in nitrogen at

300\,\text{K}

. Assume that both gases behave ideally and remain at the same pressure. Take molar masses

M_{\text{H}_{2}}=2.0\,\text{g\,mol}^{-1}

and

M_{\text{N}_{2}}=28.0\,\text{g\,mol}^{-1}

. For a rough estimate, use

\gamma =1.40

for both gases. (i) Write the expression for the speed of sound in an ideal gas, clearly identifying each symbol used. (ii) Calculate the temperature (in

^\circ\!\text{C}

) at which hydrogen must be kept so that its speed of sound equals that of nitrogen at

300\,\text{K}

. (iii) Comment briefly on whether such a temperature is practically attainable under ordinary laboratory conditions.

Related theory

Kinetic Theory of Gases
Sound Wave Characteristics
Kinetic theory of pressure
Kinetic theory of an ideal gas
Kinetic Theory

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