Question

How much the speed of sound increases by for every 1C increase

Answer 1

The speed of sound in air increases by approximately 0.6 meters per second (m/s) for every 1 degree Celsius increase in temperature.

How did we arrive at this assertion?

The relationship between the speed of sound and temperature in air is influenced by the properties of the air and can be explained through the ideal gas law and the adiabatic process. The speed of sound
`(\(v\))` in air is given through the formula:

`\[ v = √(\gamma \cdot R \cdot T) \]`

where:

-
`\( \gamma \)` is the adiabatic index (approximately 1.4 for dry air),

-
`\( R \)` is the specific gas constant for dry air,

-
`\( T \)` is the absolute temperature in kelvin.

The ideal gas law,
`\(PV = nRT\)`, relates pressure
`(\(P\))`, volume
`(\(V\))`, temperature
`(\(T\))`, and the gas constant
`(\(R\))`. For an adiabatic process, the relationship between these variables is
`\(PV^\gamma = \text{constant}\)`, where
`\( \gamma \)` is the adiabatic index.

Combining these equations, you can derive the relationship between the speed of sound and temperature:

`\[ v = √(\gamma \cdot R \cdot T) \]`

When expressing temperature in degrees Celsius, the relationship is often simplified to a rule of thumb that the speed of sound increases by approximately 0.6 meters per second for every 1 degree Celsius increase in temperature.

Complete question:

How much the speed of sound increases by for every 1C increase in temperature?