Final answer:
Use the formula f = v / λ to calculate the frequency. The frequency of the sound waves is approximately 257.25 Hz.
Step-by-step explanation:
To determine the frequency of the sound waves, we can use the formula: nλ = 2d, where n is the order of the interference, λ is the wavelength, and d is the distance between the speakers.
Given that n = 3, d1 = 7.00 m, and d2 = 9.00 m, we can rearrange the formula to solve for the wavelength:
3λ = 2(9.00 - 7.00)
Simplifying, we get: 3λ = 2(2.00)
Therefore, λ = 4.00 / 3 meters.
Since the frequency f of a wave is equal to the velocity v divided by the wavelength λ (f = v / λ), and the velocity of sound in air is approximately 343.00 m/s, we can calculate the frequency:
f = 343.00 / (4.00 / 3)
The frequency of the sound waves is approximately 257.25 Hz.