At what temperature, in degrees Celsius, is the speed of sound in air 341 m/s?
Vs = 332 + 0.6T.
341 = 332 + 0.6T,
T = 15 degrees Celsius.
The temperature outside is 20° Celsius. What is the speed of a sound in air at this temperature?
The speed of sound in air depends on temperature and other factors. However, as a rough estimate, the speed of sound in air at sea level and room temperature (about 20 degrees Celsius) is approximately 343 meters per second.
To find the temperature at which the speed of sound in air is 341 m/s, we can use a linear approximation:
Let's assume that the relationship between temperature and the speed of sound is linear. We can take two data points to form a linear equation and use that equation to find the temperature at a given speed of sound.
Data Point 1: Speed of sound = 343 m/s at 20°C
Data Point 2: Speed of sound = 341 m/s (given)
Now, using the formula for a linear equation (y = mx + b) where y represents the speed of sound, x represents the temperature, m is the slope, and b is the y-intercept, we can solve for the temperature:
m = (speed2 - speed1) / (temp2 - temp1)
= (341 - 343) / (temp2 - 20)
= -2 / (temp2 - 20)
Now, we can substitute the given speed of sound (341 m/s) and solve for the temperature (x):
341 = (-2 / (x - 20)) * (20) + 343
341 = -40 / (x - 20) + 343
-2 = -40 / (x - 20)
2(x - 20) = -40
2x - 40 = -40
2x = 0
x = 0 / 2
x = 0
So, at a temperature of 0 degrees Celsius, the speed of sound in air would be approximately 341 m/s. However, please note that this is a linear approximation, and the actual relationship between temperature and the speed of sound is more complex.
To calculate the temperature at which the speed of sound in air is 341 m/s, we can use the equation for calculating the speed of sound in air given the temperature. The equation is:
v = sqrt(gamma * R * T),
where:
- v is the speed of sound in air,
- gamma is the adiabatic index (approximately 1.4 for air),
- R is the specific gas constant for air (around 287 J/(kg·K)),
- T is the temperature in Kelvin.
To convert degrees Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15.
So, let's rearrange the equation to solve for T:
T = (v^2) / (gamma * R).
Now, we can plug in the given values:
v = 341 m/s,
gamma = 1.4,
R = 287 J/(kg·K).
Substituting these values into the equation, we can calculate T:
T = (341^2) / (1.4 * 287).
Calculating this expression gives us:
T ≈ 185.41 K.
Finally, to convert Kelvin back to degrees Celsius, we subtract 273.15 from the value:
T ≈ -87.74 °C.
Therefore, the temperature at which the speed of sound in air is 341 m/s is approximately -87.74 °C.