Question

can anyone derive this?

Answer 1

\[V _{sound}=331*\sqrt{\frac{ T }{ 273 }}\]

Answer 2

@Michele_Laino

Answer 3

@IrishBoy123

Answer 4

@ganeshie8

Answer 5

@satellite73

Answer 6

@misty1212

Answer 7

@lalaly

Answer 8

@AlexandervonHumboldt2

Answer 9

The actual derivation of this formula is not that easy. Here is a link which shows how it is done.

https://upload.wikimedia.org/wikipedia/commons/e/eb/Introduction_to_Physical_Chemistry_Lecture_5_Supplement.pdf

The interesting thing is that the speed of sound in air is of the same order of magnitude as the average speed of air molecules. This is because information (the sound wave) is communicated through the air via collisions between air molecules. The faster an air molecule is moving the quicker it will collide with another air molecule and the quicker will the sound wave travel.
The average kinetic energy of air molecules is proportional to the temperature in kelvin.
Kinetic energy depends on velocity squared, so the velocity depends on the square root of the temperature in kelvin.

Answer 10

i m reading, wait..

Answer 11

@Farcher
So, I guess its related with Thermodynamics?

Answer 12

Very much so.
In solids the speed of sound is faster because the interaction between the molecules is via bonds which propagate information quicker.

Answer 13

okay, thank you. I will take my time reading through the link you have given and also compare while studing thermodynamics

Answer 14

There are many other sources for the derivation. It is a standard derivation in university Physics courses.