Answer :
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:
[tex]\[ \text{Speed of Sound} = 331.3 + 0.606 \times \text{Temperature} \][/tex]
Given the temperature of [tex]\( 27.0 \)[/tex] °C:
1. Start with the known base speed of sound at 0 °C, which is [tex]\( 331.3 \)[/tex] m/s.
2. Next, account for the increase in speed due to the temperature. For each degree Celsius, the speed of sound increases by [tex]\( 0.606 \)[/tex] m/s.
3. Multiply the increment rate ([tex]\( 0.606 \)[/tex] m/s per °C) by the given temperature ([tex]\( 27.0 \)[/tex] °C).
Let's perform the calculation:
[tex]\[ 0.606 \times 27.0 = 16.362 \][/tex]
Now, add this value to the base speed of sound:
[tex]\[ 331.3 + 16.362 = 347.662 \text{ m/s} \][/tex]
Thus, the speed of sound in air at a temperature of 27.0 °C is approximately [tex]\( 347.662 \)[/tex] 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 [tex]\( 347.662 \)[/tex] m/s is:
a) 348 m/s
Therefore, the correct answer is:
a) 348 m/s
[tex]\[ \text{Speed of Sound} = 331.3 + 0.606 \times \text{Temperature} \][/tex]
Given the temperature of [tex]\( 27.0 \)[/tex] °C:
1. Start with the known base speed of sound at 0 °C, which is [tex]\( 331.3 \)[/tex] m/s.
2. Next, account for the increase in speed due to the temperature. For each degree Celsius, the speed of sound increases by [tex]\( 0.606 \)[/tex] m/s.
3. Multiply the increment rate ([tex]\( 0.606 \)[/tex] m/s per °C) by the given temperature ([tex]\( 27.0 \)[/tex] °C).
Let's perform the calculation:
[tex]\[ 0.606 \times 27.0 = 16.362 \][/tex]
Now, add this value to the base speed of sound:
[tex]\[ 331.3 + 16.362 = 347.662 \text{ m/s} \][/tex]
Thus, the speed of sound in air at a temperature of 27.0 °C is approximately [tex]\( 347.662 \)[/tex] 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 [tex]\( 347.662 \)[/tex] m/s is:
a) 348 m/s
Therefore, the correct answer is:
a) 348 m/s
