What is the speed of a sound wave from a 440 Hz tuning fork at temperature 23 degrees C?

Question

What is the speed of a sound wave from a 440 Hz tuning fork at temperature 23 degrees C?

Answer 1

The speed of sound will depend only on the properties of the air.  The frequency and wavelength will then be subject to:

 

wavelength * frequency = speed

 

The speed of sound in an ideal gas of specific heat ratio gamma and average molecular weight M is:

 

v = sqrt[gamma * (R/M) * T]

 

where R is the universal gas constant = 8.31 J / (mol K), and T is in Kelvin

 

For air, gamma = 1.4 and M = 28.8 g/mol = 28.8 x 10^-3 kg/mol

 

At T = 23 degrees C = 296 K,

 

v = sqrt(1.4 * {[8.31 J/(mol K)] / (28.8 x 10^-3 kg/mol)} * 296 K) m/s = 345.8 m/s

 

Then wavelength = speed / frequency = (345.8 m/s ) / (440 Hz) = 0.7859 m

 

 

Answer 2

The speed (m/s) of a sound wave in air at a temperature T Kelvins is given by

VT = 331 √ (T/273)

Change 23 degrees Celsius to Kelvins, and substitute in the above equation.