QuestionJuly 2, 2025

Required information What is the speed of sound, in ft/s if the air temperature is: 96.4^circ C square ft/s

Required information What is the speed of sound, in ft/s if the air temperature is: 96.4^circ C square ft/s
Required information What is the speed of sound, in ft/s if the air temperature is: 96.4^circ C square ft/s

Solution
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Answer

1229.35 \, ft/s Explanation 1. Convert Celsius to Fahrenheit Use the formula F = \frac{9}{5}C + 32. For C = 96.4, F = \frac{9}{5} \times 96.4 + 32 = 205.52. 2. Calculate Speed of Sound in Air Use the formula for speed of sound in air: v = 1086 \sqrt{\frac{T + 459.67}{518.67}}, where T is in Fahrenheit. Substitute T = 205.52: v = 1086 \sqrt{\frac{205.52 + 459.67}{518.67}}. 3. Simplify and Compute Calculate inside the square root: \frac{665.19}{518.67} \approx 1.282. Then, v = 1086 \times \sqrt{1.282} \approx 1086 \times 1.132 = 1229.352.

Explanation

1. Convert Celsius to Fahrenheit<br /> Use the formula $F = \frac{9}{5}C + 32$. For $C = 96.4$, $F = \frac{9}{5} \times 96.4 + 32 = 205.52$.<br /><br />2. Calculate Speed of Sound in Air<br /> Use the formula for speed of sound in air: $v = 1086 \sqrt{\frac{T + 459.67}{518.67}}$, where $T$ is in Fahrenheit. Substitute $T = 205.52$: <br />$v = 1086 \sqrt{\frac{205.52 + 459.67}{518.67}}$.<br /><br />3. Simplify and Compute<br /> Calculate inside the square root: $\frac{665.19}{518.67} \approx 1.282$.<br /> Then, $v = 1086 \times \sqrt{1.282} \approx 1086 \times 1.132 = 1229.352$.
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