Question

The range of audible frequencies is from about 20 Hz to 20,000 Hz. What is the range of the wavelengths of audible sound in air?

A) 1.7×1041.7×10 4m to 1.7×107×10 7m
B) 3×1073×10 7m to 3×1093×10 9m
C) 1×10−41×10 −4m to 1×1−21×10 −2m
D) 1.5×10−11.5×10 −1m to 1.5×1041.5×10 m

Answer 1

The range of wavelengths for audible sounds in air, given the speed of sound is 344 m/s, is from 17.2 meters at the low frequency of 20 Hz to 1.72 centimeters at the high frequency of 20,000 Hz.

Step-by-step explanation:

To calculate the range of wavelengths of audible sound in air, we can use the formula for the speed of sound:

Speed of Sound (v) = Frequency (f) × Wavelength (λ)

Given the speed of sound in air is approximately 344 m/s (at room temperature), we are able to calculate the wavelengths for the extremes of the human audible spectrum, which are 20 Hz and 20,000 Hz.

For the lowest audible frequency (20 Hz):

λ = v / f
λ = 344 m/s / 20 Hz
λ = 17.2 m

For the highest audible frequency (20,000 Hz):

λ = v / f
λ = 344 m/s / 20,000 Hz
λ = 0.0172 m or 1.72 cm

Therefore, the wavelength range for audible sounds is from 17.2 meters for the lowest frequency to 1.72 centimeters for the highest frequency.