Final answer:
To calculate the frequency, we can use the formula for destructive interference in sound waves, which involves the harmonic number, wavelength, and path length difference. By substituting the given values and solving the equation, the frequency is determined to be 114.33 Hz.
Step-by-step explanation:
To determine the frequency, we can use the formula for destructive interference in sound waves:
nλ = 2d
where n is the harmonic number (in this case, 1), λ is the wavelength of the sound wave, and d is the path length difference between the two speakers. The path length difference can be calculated by subtracting the distance of the closer speaker from the distance of the farther speaker:
d = 5.20 m - 3.70 m = 1.50 m
Substituting the values into the formula, we have:
1 * λ = 2 * 1.50 m
λ = 3.00 m
Therefore, the frequency of the sound wave is:
f = v / λ
f = 343.00 m/s / 3.00 m = 114.33 Hz