Question

the speed of the sound through air is linearly related to the temperature of the air. if sounds travel at 325m/secs at 0°C and at 340m/sec at 30°C, construct a linear model relating the speed of sound (s) and the air temperature (t). interpret the slope of this model

Answer 1

Let the speed of sound be C

C=kT+B

Where T is the temperature,

At T= 0 degrees, C=325 m/s

325=0T+B,

B=325

C=kT+325

Let us use the second information to find k

At T=30 degrees, C=340m/s

340=k(30) +325

30k=340-325 =15

30k=15

k=0.5

Our full linear model is

C=0.5T+325

Therefore, our slope is k= 0.5

The intercept = 325m/s