Question

Which of the following statements is wrong?
A. Changes in air temperature have no effect on the speed of sound
B. Changes in air pressure have on effect on the speed of sound
C. The speed of sound in water is higher than in air
D. The speed of light in water is lesser than in air

Answer 1

Hint: Factor on which speed of sound depends and how it changes from laplace formula of speed of sound.

Formula used $V = \sqrt {\dfrac{{rP}}{\rho }} $

Complete step by step answer:
We know that laplace formula for the speed of sound in a gas is
$V = \sqrt {\dfrac{{rP}}{\rho }} $…………. (I)
Where, $V = $ is the speed of sound in a gas
$r = $ratio of specific heats
$P = $Pressure
$\rho = $density
Effect of temperature
Now, for one mole of a gas, ideal gas equation given by
$PV = RT$……. (as $n = 1$)
Where $R$ is gas constant and $T$ is absolute temperature
If $M$ is the molecular mass of the gas and $P$ is its density, then
Density $ = \dfrac{{Mass}}{{Volume}}$
$
   \Rightarrow \rho = \dfrac{M}{V} \\
   \Rightarrow V = \dfrac{M}{\rho } \\
 $
Therefore, $\dfrac{{PM}}{\rho } = RT$
$ \Rightarrow \dfrac{P}{\rho } = \dfrac{{RT}}{M}$…………….. (II)
Put (II) in (I), we get
$V = \sqrt {\dfrac{{rRT}}{M}} $
Clearly, $V \propto \sqrt T $
Hence, the speed of sound in a gas is directly proportional to square root of its absolute temperature.
So, for air, speed of sound is directly proportional to temperature.
Hence option (A) is a wrong statement.
Effect of pressure:
$V = \sqrt {\dfrac{{rP}}{\rho }} $
At constant temperature, $PV = $ constant
$\dfrac{{Pm}}{\rho } = $constant $\left\{ {\because P = \dfrac{m}{V}{\text{ or V = }}\dfrac{M}{\rho }} \right\}$
Since $M$ is constant
So, $\dfrac{P}{\rho } = $constant
Therefore, pressure has no effect
Hence, the correct option is B.

Note:Speed of light $ \propto \dfrac{1}{{density}}$
That’s why the speed of light is lesser than in air as density of water is more than air.