# 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.

## Answers and Replies

Homework Helper
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