Question

What is the speed of sound?
(a) in water
(b) in air
(c) in iron

Answer 1

Hint:The sound propagates in the form of longitudinal waves and the speed of sound depends upon the medium of travel, that's why the value of speed of sound changes with the type of medium. For example, the value of the speed of sound in water is different from the value of speed of sound in air because of the density difference between water and air.So, the speed of sound gets faster as the medium gets denser, that is why the sound's speed in water is more than the speed of water in air.

Complete step by step answer:
-For water,
The speed of sound in water is approximately \[1480{\rm{ m/s}}\] at room temperature \[\left( {20{\text{ to 25}}^\circ {\rm{C}}} \right)\].
-For air,
The speed of sound in air is approximately \[{\text{331}}{\text{.5 m/s at 0}}^\circ {\text{ C}}\] temperature.
-For iron,
The speed of sound in iron is approximately \[{\rm{5120 m/s}}\] at room temperature \[\left( {20{\text{ to 25}}^\circ {\rm{C}}} \right)\].
Therefore, the speed of sound:
(a) in water \[ = 1480{\rm{ m/s}}\]
(b) in air $ = {\rm{331}}{\rm{.5 m/s}}$
(c) in iron $ = {\rm{5120 m/s}}$

Note: The alternate method to calculate the speed of sound -
The speed of sound $v$ in air at temperature $T$ is given by this formula-
$v = \sqrt {\gamma RT} $
Where, $\gamma $ the specific heat ratio of air and its value is $\gamma = 1.4$
$R$ is the characteristic gas constant of air and its value $R = 287{\rm{ J/kgK}}$
And, $T$ is the temperature of air in Kelvin.
At $0^\circ C{\text{ or 273K}}$ air temperature, the speed of sound is –
$\begin{array}{l}
\Rightarrow v = \sqrt {1.4 \times 287 \times 273} \\
\Rightarrow v = \sqrt {109691.4} \\
\Rightarrow v = 331.2{\rm{ m/s}}
\end{array}$