Hello,

I am kind stuck on this question

In the lab you discover a relationship between the temperature of the air and the speed of sound. You find the speed of sound is never lower than 331 m/s and increases by 60% of the current temperature.

a. What is the equation from this relationship?
b. If the temperature is 300 C, what is the speed of sound?
c. If the speed of sound is 391 m/s, what must be the temperature?

s = 331 + .6t

s(300) = 331 + .6(300) = 331 + 180 = 511

391 = 331 + .6t
60 = .6t
100 = t

Hello,

I can help you with your questions. Let's go through each one step by step:

a. What is the equation from this relationship?

To find the equation, we need to first understand the relationship between temperature and speed of sound given in the problem statement. The problem states that the speed of sound increases by 60% of the current temperature.

So, if we let T represent the temperature in degrees Celsius, and S represent the speed of sound in m/s, the equation for this relationship can be written as:

S = 331 + 0.6T

Here, 331 is the minimum speed of sound (when the temperature is 0 degrees Celsius) and 0.6T represents the increase in speed of sound based on the temperature.

b. If the temperature is 300 C, what is the speed of sound?

To find the speed of sound when the temperature is 300 degrees Celsius, we can substitute T = 300 into the equation we derived in the previous step:

S = 331 + 0.6(300)
S = 331 + 180
S = 511 m/s

Therefore, when the temperature is 300 degrees Celsius, the speed of sound is 511 m/s.

c. If the speed of sound is 391 m/s, what must be the temperature?

To find the temperature when the speed of sound is 391 m/s, we can rearrange the equation we derived in step a:

S = 331 + 0.6T

Substituting S = 391 into the equation, we can solve for T:

391 = 331 + 0.6T
60 = 0.6T
T = 100

Therefore, when the speed of sound is 391 m/s, the temperature must be 100 degrees Celsius.

I hope this helps! Let me know if you have any further questions.