Determine the frequency of beats produced in air when two sources...

Given:

Speed of sound, $v = 350 \text{ m/s}$

Wavelength of first source, $\lambda_1 = 32 \text{ cm} = 0.32 \text{ m}$

Wavelength of second source, $\lambda_2 = 32.2 \text{ cm} = 0.322 \text{ m}$

The frequencies of the sound produced by the two sources are:

$f_1 = \dfrac{v}{\lambda_1} = \dfrac{350}{0.32} = 1093.75 \text{ Hz}$

$f_2 = \dfrac{v}{\lambda_2} = \dfrac{350}{0.322} \approx 1086.96 \text{ Hz}$

The beat frequency is the difference between the two frequencies:

$f_{beat} = f_1 - f_2 = 1093.75 - 1086.96 = 6.79 \text{ Hz}$

Rounding to the nearest integer, the beat frequency is approximately $7 \text{ Hz}$.