The lower frequency limit for human hearing is usually considered to be 20.0 Hz. (a) What is
the speed of sound in m/s if the air temperature is 20.0ºC? (b) What is the corresponding
wavelength for this frequency?
Do you know the difference between psychics and physics? I hope so!
To find the speed of sound at a given temperature, we can use the formula:
v = sqrt(γ * R * T)
Where:
v = speed of sound
γ = adiabatic index (for air, it's typically around 1.4)
R = gas constant (for air, it's approximately 287 J/(kg·K))
T = temperature in Kelvin (convert Celsius to Kelvin by adding 273.15)
(a) Calculation for the speed of sound:
Given that the air temperature is 20.0ºC, we need to convert it to Kelvin:
T = 20.0 + 273.15 = 293.15 K
Substituting the values into the formula:
v = sqrt(1.4 * 287 * 293.15)
v = sqrt(122727.1)
v ≈ 350.5 m/s
Therefore, the speed of sound in air at a temperature of 20.0ºC is approximately 350.5 m/s.
(b) Calculation for the corresponding wavelength:
The wavelength (λ) is related to the speed of sound (v) and frequency (f) by the formula:
λ = v / f
Given that the lower frequency limit for human hearing is 20.0 Hz, we can calculate the wavelength:
λ = 350.5 m/s / 20.0 Hz
λ ≈ 17.5 m
Hence, the corresponding wavelength for a frequency of 20.0 Hz is approximately 17.5 meters.