Final answer:
The frequency of the sound waves is 137.2 Hz.
Step-by-step explanation:
To calculate the frequency of the sound waves in this situation, we can use the formula:
f = v / λ
where f is the frequency, v is the velocity of sound (343 m/s), and λ is the wavelength. Since the speakers are identical and the interference is constructive at n = 1, the path difference between the two speakers will be equal to one wavelength.
We can calculate the path difference using the formula:
Δx = x2 - x1
where x2 is the distance from the second speaker (5.20 m) and x1 is the distance from the first speaker (2.70 m).
Substituting these values into the formula, we get:
Δx = 5.20 m - 2.70 m = 2.50 m
Since constructive interference occurs at a path difference equal to one wavelength, we can set the path difference equal to the wavelength and solve for the frequency:
2.50 m = λ
f = v / λ = 343 m/s / 2.50 m = 137.2 Hz