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Question

The relation between speed of sound in moist air vm and dry air vd at the same temperature and pressure will be

A
vm<vd
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B
vm>vd
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C
vm=vd
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D
vmvd
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Solution

The correct option is B vm>vd
We know that the speed of sound in air is given by,

v=γPρ=γRTM

At the same temperature and pressure of air,

v1M .....(1)

Dry air mostly contains nitrogen (78%) and oxygen (21%) and other gases like CO2 in traces.

Moist air will contain a higher volume fraction of moisture. The moisture will replace some of the volume occupied by gases like CO2, N2, O2, etc.

Molar mass of H2O is 18 g/mol, which is lesser than the constituent components of dry air.

This will lead to reduction in the effective molar mass of the moist airMmoist air<Mdry air.

Md>Mm .....(2)

From equation (1) and (2) we get,

vm>vd

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