Question

the speed of sound in air is about 332 meters per second (m/s) at 0 degrees celsius (°c). if the speed increases by 0.6 m/s for every increase in temperature of 1°c, which inequality best represents the temperatures, t, in degrees celsius, for which the speed of sound in air exceeds 350 m/s? choose 1 answer: a t < 30 b t ≤ 30 c t > 30 d t ≥ 30

Explanation:

Step1: Set up the speed - temperature relationship

The speed of sound $v$ at temperature $T$ (in $^{\circ}C$) is given by the linear equation $v = 332+0.6T$ (since the initial speed at $T = 0^{\circ}C$ is $332\frac{m}{s}$ and it increases by $0.6\frac{m}{s}$ per $1^{\circ}C$ increase in temperature).

Step2: Set up the inequality

We want to find when the speed of sound exceeds $350\frac{m}{s}$, so we set up the inequality $332 + 0.6T>350$.

Step3: Solve the inequality

Subtract 332 from both sides: $0.6T>350 - 332$, so $0.6T>18$. Then divide both sides by 0.6: $T>\frac{18}{0.6}=30$.

Answer:

C. $T > 30$