To determine the approximate speed of sound in air at a temperature of 27.0 °C, we can use the formula that relates the speed of sound to the temperature in Celsius:
\(\[ \text{Speed of Sound} = 331.3 + 0.606 \times \text{Temperature} \]\)
Given the temperature of \(\( 27.0 \)\) °C:
1. Start with the known base speed of sound at 0 °C, which is \(\( 331.3 \)\) m/s.
2. Next, account for the increase in speed due to the temperature. For each degree Celsius, the speed of sound increases by \(\( 0.606 \)\) m/s.
3. Multiply the increment rate (\(\( 0.606 \)\) m/s per °C) by the given temperature (\(\( 27.0 \)\) °C).
Let's perform the calculation:
\(\[ 0.606 \times 27.0 = 16.362 \]\)
Now, add this value to the base speed of sound:
\(\[ 331.3 + 16.362 = 347.662 \text{ m/s} \]\)
Thus, the speed of sound in air at a temperature of 27.0 °C is approximately \(\( 347.662 \)\) m/s.
Given the provided options:
a) 348 m/s
b) 304 m/s
c) 358 m/s
d) 315 m/s
The closest approximate value to \(\( 347.662 \)\) m/s is:
a) 348 m/s
Therefore, the correct answer is:
a) 348 m/s
