The speed of sound through air is linearly related to the temperature of the air

Question

The speed of sound through air is linearly related to the temperature of the air. If sound travels at 326 m/sec at 0 degrees celcius and at 332 m/ sec at 20 degrees celcius.

1. Construct a lineral model relating the speed of sound (s) and the air temperatue (t). Interpret the slope of this model.

s=

2. Interpret the slope of this model

a) The rate of change of speed of soumd with respect to tempature is 0.3 m/ sec per degrees celcius

b) The rate of change of speed of sound with respect to temperature is 16.6 m/ sec per degrees celcius

c) The rate of change of speed of sound with respect to temperature is 20 m/ sec per degrees celcius

d) The rate of change of speed of sound with respect to temperature is 6 m/sec per degrees celcius

Explanation / Answer

The speed of sound through air is linearly related to the temperature of the air. If sound travels at 326 m/sec at 0 degrees celcius and at 332 m/ sec at 20 degrees celcius.

1. Construct a lineral model relating the speed of sound (s) and the air temperatue (t). Interpret the slope of this model.

From the word problem pull out the two points (0,326) and (20,332). Use these to find the slope of the linear model.

(332-326)/(20-0) so slope is 0.3 m/sec/deg or change of speed of sound per degree change in temperature

plugging this into the point slope equation for a line where y=s and x=t

s-326 = .3(t-0)

the linear model is s = 0.3t + 326

2. Interpret the slope of this model

a) The rate of change of speed of soumd with respect to tempature is 0.3 m/ sec per degrees celcius

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