Question

The speed of sound in air at \[0\;{\rm{^\circ C}}\]is \[332\;{\rm{m/s}}\]. The speed of sound in air at \[35\;{\rm{^\circ C}}\] will be:
A. \[325\;{\rm{m/s}}\]
B. \[332\;{\rm{m/s}}\]
C. \[353\;{\rm{m/s}}\]
D. \[367\;{\rm{m/s}}\]

Answer 1

Hint: The above problem can be resolved using the mathematical relation for the velocity of sound at any range of temperature of the air. The velocity of sound depends on the medium and also on the temperature of the surround. Moreover, in the given problem, we have the velocity of sound at zero degrees, then substituting the value, we can get the value of the velocity of sound in air at the desired temperature.

Complete step by step answer:
Given:
The speed of sound in air at \[0\;{\rm{^\circ C}}\] is \[332\;{\rm{m/s}}\].
We know that the speed of the sound varies directly with the value of temperature. Therefore, the expression for the speed of sound in air at temperature T is,
\[v\left( t \right) = {v_0} + 0.61T\]
Here, \[{v_0}\] is the speed of sound \[0\;^\circ {\rm{C}}\] and T is the temperature, at which the speed of sound is to be determined and its value is \[35{\rm{^\circ C}}\].
Solve by substituting the value in the above expression as,
\[\begin{array}{l}
v\left( t \right) = 332\;{\rm{m/s}} + 0.61 \times \left( {35{\rm{^\circ C}}} \right)\\
v\left( t \right) = 353.35\;{\rm{m/s}}\\
v\left( t \right) \approx 353\;{\rm{m/s}}
\end{array}\]
Therefore, the speed of sound at \[35{\rm{^\circ C}}\] is \[353\;{\rm{m/s}}\] and option (C) is correct.

Note:To resolve the given problem, one must clear the basic fundamental regarding the velocity of sound in a different medium. The velocity of sound keeps on changing if the temperature of the medium of propagation tends to change. Moreover, the speed of sound has its basic formula related to the temperature, which needs to be kept in mind, to solve the typical problems.