Question

Calculate the wavelengths (m) of sounds in 30 degrees F air at the extremes of the audible frequency range of a young, normal-hearing human ear (i.e., highest and lowest frequency sounds we can hear). i know the highest is 20,000 hz and the lowest is 20 hz but I have no idea how to solve involving temperature.

Answer 1

The speed of sound depends on the temperature.

in air, the relation between speed of sound and temperature is given by the equation

V_ST = 331.3 m/s + 0.6 T m/s

Where V_ST = speed of sound at temperature T.

T - temperature in degree Celsius.

Given

T = 30 degree F

Convert degree F into degree Celsius.

The convertion formula is

C/100 =( F - 32 )/180

Where C- temperature in degree Celsius

F- temperature in degree faren

Substituting

C /100 = (30-32)/180 = -1 /90

C = -100/90 = -1.11 degree Celsius

Substituting in equation for speed of sound

V_ST = 331.3 + 0.6×(-1.11) = 331.3 - 0.67 = 330.63 m/s

For a wave the relation between speed,wavelength and frequency is

Speed = frequency × wavelength

Hence wavelength = Speed / frequency

Now at highest Audible frequency

Speed = 330.63 m/s

Frequency = 20,000 Hz

Wavelength = 330.63/20,000 = 1.65 ×10^-2 m

At lowest Audible frequency

Frequency = 20 Hz

Wavelength = 330.63 /20 = 16.5 m