(a) The speed of sound in air at a given temperature can be calculated using the following formula:
v = 331.4 + 0.6 * T
where v is the speed of sound in m/s, and T is the air temperature in ºC.
For an air temperature of 20.0ºC:
v = 331.4 + 0.6 * 20.0
v ≈ 343.4 m/s
The speed of sound in air at 20.0ºC is approximately 343.4 m/s.
(b) To find the wavelength corresponding to the lower frequency limit for human hearing (20.0 Hz), we can use the formula:
λ = v / f
where λ is the wavelength, v is the speed of sound in m/s, and f is the frequency in Hz.
λ = 343.4 m/s / 20.0 Hz
λ ≈ 17.17 m
The corresponding wavelength for the lower frequency limit for human hearing at 20.0ºC is approximately 17.17 meters.