Question
What is the effect of humidity on sound waves when humidity increases?
A.
Speed of sound waves increases
B.
Speed of sound waves decreases
C.
Speed of sound waves remains same
D.
Speed of sound waves becomes zero
Answer :
Speed of sound waves increases
Solution :
The presence of water vapours in air changes its density. That is why the velocity of sound changes with humidity of air.
Suppose,
$${\rho _m} = $$ density of moist air
$${\rho _d} = $$ density of dry air
$${v_m} = $$ velocity of sound in moist air
$${v_d} = $$ velocity of sound in dry air
Assuming that effect of humidity on $$\gamma $$ is negligible.
As velocity of wave in a medium is given by
\[\therefore {v_m} = \sqrt {\frac{{\gamma p}}{{{\rho _m}}}} \,\,\left[ {\begin{array}{*{20}{c}}
{\gamma = {\text{elasticity of medium}}} \\
{{\rho _m} = {\text{density of medium}}} \\
{p = {\text{pressure of sound waves}}}
\end{array}} \right]\]
$$\eqalign{
& {\text{and}}\,\,{v_d} = \sqrt {\frac{{\gamma p}}{{{\rho _d}}}} \cr
& {\text{Dividing, we get }}\frac{{{v_m}}}{{{v_d}}} = \sqrt {\frac{{{\rho _d}}}{{{\rho _m}}}} \cr} $$
The presence of water vapours reduces the density of air.
$${\text{i}}{\text{.e}}{\text{.}}\,{\rho _m} < {\rho _d}$$
Hence, velocity of sound in moist air is greater, then the velocity of sound in dry air.