Answer:
Frequency at minimum intensity 0.17 m from center = 500 Hz
Frequency at maximum intensity 0.17 m from center = 1000 Hz
Explanation:
a. Frequency at minimum intensity 0.17 m from center
Since we move 0.17 m away from the center to encounter a minimum, the distance between the first speaker and that point is d₁ = 2 + 0.17 = 2.17 m. The distance between the second speaker and that point is d₂ = 2 - 0.17 = 1.83 m.
The path difference between the two waves is Δd = d₁ - d₂ = 2.17 m - 1.83 m = 0.34 m
Since we have a minimum at this point, there is destructive interference, so Δd = (m + 1/2)λ where λ = wavelength of wave m = 0,1,2...
when m = 0, we have
Δd = (0 + 1/2)λ = 1/2λ
λ = 2Δd = 2 × 0.34 m = 0.68 m.
The frequency of the wave is thus f = v/λ where v = speed of sound = 340 m/s. f = 340 m/s÷ 0.68 m = 500 Hz
b. Frequency at maximum intensity 0.17 m from center
If the frequency is increased while you remain at 0.17 m a maximum sound intensity is observed when the path difference Δd = mλ m = 0,1,2...
When m = 1, Δd = 0.34 m = λ
Frequency, f = v/λ = 340m/s ÷ 0.34 m = 1000 Hz = 1 kHz
