Question

The speed of sound waves at 300K is 332m/s. At what temperature will the speed be $574m/s$.

Answer 1

The speed of sound is the distance traveled per unit time by any sound. Sound speed is defined as the strong distribution of sound waves. This depends on the signs of the way in which the expansion occurs. The speed of sound is used for describing the speed of sound waves in an elastic medium.
Velocity of sound depends up on the temperature that is,
$velocity{\text{ }}of{\text{ }}sound{\text{ }}\left( {{\text{ }}V} \right) \propto temperature{\text{ }}\left( T \right)$
When temperature is increased then energy of molecules also increase due to which molecule vibrate with greater speed and velocity of sound increase

Complete step by step solution:
The velocity of sound at specific temperature is given by
$V = 331\sqrt {\dfrac{T}{{273}}}$
We want value of $T$ so we have to take it out hence we get
$T = {\left( {\dfrac{V}{{331}}} \right)^2} \times 273K$
In the question we have the value of velocity that is $V = 574m/s$ substitute that in the above equation
$T = {\left( {\dfrac{{574}}{{331}}} \right)^2} \times 273K$
After solving the above equation we get
$T = 2.99 \times 273K$
After simplifying we get
$T = 816.27K$

Note:
I would like to let you know that the speed of sound changes by $0.6m/s$ for every $1^\circ$ change in temperature.
Velocity is the derivative of the displacement with respect to the time. Displacement is a measure of how much an object can change the position. So velocity is the rate of change of the position, that is how fast something moves and where it’s headed. If you know how far something has moved, in which direction, and how long it took,
Sound waves are longitudinal waves that travel in the middle like air or water. When we think of sound, we often think about how big it is (amplitude, or intensity) and its height (frequency).