Question

The speed of sound in dry air at 20° C (68° F) is 1.236 × 103 km/h. What is the speed of sound written as an ordinary number?

Answer 1

Step-by-step explanation:

The speed of sound has nothing to do with "sea level" and sound pressure and without the medium air there is no speed of sound. In SI units with dry air at 20°C (68°F), the speed of sound c is 343 meters per second (m/s). This also equates to 1235 km/h, 767 mph, 1125 feet per second (ft/s), or 666 knots.

Answer 2

The speed of sound in dry air at 20°C (68°F) is approximately 1.236 × 10^3 km/h.

Step-by-step explanation:

The speed of sound can be calculated using the formula:

`\[ \text{Speed} = \sqrt{(\gamma \cdot R \cdot T)/(M)} \]`

where:

`- \( \gamma \) is the adiabatic index (for dry air, \( \gamma \approx 1.4 \)),`

`- \( R \) is the specific gas constant (\( R \approx 287 \, \text{J/(kg} \cdot \text{K)} \)),`

`- \( T \) is the temperature in Kelvin (\( T = 20 + 273.15 \)),`

`- \( M \) is the molar mass of air (\( M \approx 0.029 \, \text{kg/mol} \)).`

Substituting the given values into the formula:

`\[ \text{Speed} = \sqrt{(1.4 \cdot 287 \cdot (20 + 273.15))/(0.029)} \]`

`\[ \text{Speed} \approx \sqrt{(1.4 \cdot 287 \cdot 293.15)/(0.029)} \]`

`\[ \text{Speed} \approx \sqrt{(1.4 \cdot 83975.05)/(0.029)} \]`

`\[ \text{Speed} \approx \sqrt{(117565.07)/(0.029)} \]`

`\[ \text{Speed} \approx √(4054002.76) \]`

`\[ \text{Speed} \approx 2013.4 \, \text{m/s} \]`

Converting the speed to km/h:

`\[ \text{Speed} \approx 2013.4 * (3600)/(1000) \]`

`\[ \text{Speed} \approx 7242.24 \, \text{km/h} \]`

Therefore, the speed of sound in dry air at 20°C is approximately 1.236 × 10^3 km/h.