What is the speed of sound at this temperature?

The speed of sound at a temperature of 298K is 346 m s–1 and there is a 1.76% change in the value of the speed of sound.
  • #1
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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

[tex]\frac{340}\sqrt{288}[/tex] = [tex]\frac{V}\sqrt{298}[/tex]

V @298K = 346 m s–1
% change = 1.76%

Can someone please check if both my answers are correct? Thanks!
 
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  • #2
I don't see any problem.
 
  • #3


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!
 

1. What is the speed of sound at room temperature?

The speed of sound at room temperature, which is typically around 25°C or 77°F, is approximately 343 meters per second (m/s). This value may vary slightly depending on factors such as humidity and altitude.

2. Does the speed of sound change with temperature?

Yes, the speed of sound is directly affected by changes in temperature. As temperature increases, the speed of sound also increases. This is because sound waves travel faster through warmer air, which has a lower density compared to colder air.

3. How does the speed of sound change with altitude?

The speed of sound decreases with increasing altitude. This is because as altitude increases, the air becomes less dense, causing sound waves to travel more slowly. At higher altitudes, sound waves may also encounter less resistance and therefore travel faster.

4. What is the relationship between temperature and the speed of sound?

The speed of sound and temperature have a direct relationship. As temperature increases, the speed of sound also increases. This is because when temperature rises, the molecules in the air move faster, allowing sound waves to travel more quickly through the medium.

5. How does humidity affect the speed of sound?

Humidity can affect the speed of sound by either increasing or decreasing it, depending on the temperature and humidity levels. In general, higher levels of humidity can cause sound waves to travel slightly faster due to the presence of water vapor, which is less dense than dry air. However, at very high humidity levels, the opposite may occur and the speed of sound may decrease due to increased air density.

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