Answer:
C) 413 Hz
Step-by-step explanation:
For destructive interference, the path difference ΔL = (n + 1/2)λ where ΔL = L₂ - L₁ where L₁ = person's distance from one speaker (the closer one) = 5.0m and L₂ = person's distance from other speaker (the farther one) = 6.2 m and λ = wavelength = v/f where v = speed of sound = 330 m/s and f = frequency
So, ΔL = (n + 1/2)λ
L₂ - L₁ = (n + 1/2)v/f
f = (n + 1/2)v/(L₂ - L₁)
At the second lowest frequency that results in destructive interference at the point where the person is standing, n = 1.
So,
f = (1 + 1/2)v/(L₂ - L₁)
f = 3v/2(L₂ - L₁)
Substituting the values of the variables into the equation, we have
f = 3v/2(L₂ - L₁)
f = 3(330 m/s)/2(6.2 m - 5.0 m)
f = 3(330 m/s)/2(1.2 m)
f = 990 m/s ÷ 2.4 m)
f = 412.5 Hz
f ≅ 413 Hz