What is the speed of sound at this temperature?

[rachelle]

Homework Statement

The speed of sound in air is proportional to the square root of the temperature in kelvin. A flute player begins playing with the temperature of air in the tube at 288 K. The speed of sound at this temperature is 340 m s–1. After a few minutes playing the air temperature in the bore rises to 298 K.

What is the speed of sound at this temperature?
What is the percent change in the value of the speed of sound?2. The attempt at a solution

$$\frac{340}\sqrt{288}$$ = $$\frac{V}\sqrt{298}$$

V @298K = 346 m s–1
% change = 1.76%

Can someone please check if both my answers are correct? Thanks!

 

[Dick]

I don't see any problem.

 

[m2003]

I can confirm that your answers are correct. The speed of sound at 298K is 346 m/s and the percent change from 288K to 298K is 1.76%. This is in line with the relationship between temperature and the speed of sound, where a slight increase in temperature leads to a slight increase in the speed of sound. Great job on your calculations!