How Does Temperature Affect the Speed of Sound?

[chawki]

Homework Statement

The speed of sound in the air is proportional to the square root of the absolute temperature. At 20 °C the speed of sound is 343 m/s.

Homework Equations

What is the speed of sound at –10 °C? (0 °C = 273 K).

The Attempt at a Solution

speed of sound= x*$$\sqrt{}T$$
x*$$\sqrt{}293.15$$=343m/s
x=20.03

so the speed of sound at -10 C (263.15K) is: 20.03*$$\sqrt{}263.15$$ = 324.92m/s.

 

[tiny-tim]

hi chawki!

your answer is correct, and your method works, but it will lose you marks in the exam

you do not need to find the value of x …

the whole point of questions like this is to see whether you understand this point

you have done this in two steps: you found x, and then you eliminated x …

that is a waste of time (and introduces an opportunity for error)

the correct method (to be used in all "proportionality" cases) is:

speed at -10° C (263.17° K) = 343 x √(263.15)/√(293.15) = 324.92​

 

[chawki]

Ah the yellow fish again :P
Thank you for your help tiny-tim :)
I try to understand your method