On a hot summer day, the temperature of air in Arizona reaches 118°F. What is the speed of sound in air at this temperature? (Enter your answer to four significant figures. The speed of sound at 0°C is 331 m/s. Use the conversion 0°C = 273 K as necessary.)
To find the speed of sound in air at a given temperature, we can use the formula:
v = (331 m/s) * sqrt(T / 273 K)
where v is the speed of sound in air and T is the temperature in Kelvin.
First, we need to convert the temperature from Fahrenheit to Kelvin. The formula to convert Fahrenheit to Kelvin is:
T(K) = (T(°F) + 459.67) * (5/9)
In this case, the temperature is 118°F. Let's perform the conversion:
T(K) = (118 + 459.67) * (5/9)
≈ (577.67) * (5/9)
≈ 320.93 K
Now that we have the temperature in Kelvin, let's substitute it into the formula:
v = (331 m/s) * sqrt(320.93 K / 273 K)
≈ (331 m/s) * sqrt(1.1776)
≈ (331 m/s) * 1.084
≈ 358.8 m/s
Therefore, the speed of sound in air at a temperature of 118°F is approximately 358.8 m/s.