A sound wave has a frequency of 686 Hz in air and a wavelength of 0.50 m. What is the temperature of the air?
In order to find the temperature of the air, we need to use the formula for the speed of sound in air, which is given by:
v = f * λ
Where:
v is the speed of sound,
f is the frequency,
and λ is the wavelength.
Since we have the frequency and wavelength values, we can plug them into the formula to find the speed of sound.
v = 686 Hz * 0.50 m
v = 343 m/s
The speed of sound in air is approximately 343 meters per second.
Now, we can utilize the formula for the speed of sound in air to find the temperature of the air. The formula is given by:
v = √(γ * R * T)
Where:
v is the speed of sound in air,
γ is the adiabatic index (which is approximately 1.4 for air),
R is the gas constant for air (287 J/(kg·K)),
and T is the temperature in Kelvin.
Rearranging the formula, we get:
T = (v^2)/(γ * R)
Substituting the known values:
T = (343 m/s)^2 / (1.4 * 287 J/(kg·K))
Calculating this equation will give us the temperature of the air in Kelvin.