Question

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?

Answer 1

(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.