Final answer:
The destructive interference occurs when the path length difference between the two speakers is equal to an odd multiple of half the wavelength. The wavelength is 11 meters.
Step-by-step explanation:
When two speakers emit sound waves, they can interfere with each other. In the case of this question, the person is standing at different distances from two identical speakers. The destructive interference occurs when the path length difference between the two speakers is equal to an odd multiple of half the wavelength. For destructive interference with n = 1, the formula is:
d₁ - d₂ = (2n - 1) * λ / 2,
where d₁ is the distance to the first speaker, d₂ is the distance to the second speaker, and λ is the wavelength.
Using the given values, we can solve for the wavelength:
7.70 - 13.20 = (2 * 1 - 1) * λ / 2
-5.50 = -λ / 2
λ = 11 m.
Therefore, the wavelength is 11 meters.