Answer:
f = 147.21 Hz
Explanation:
In order to have a destructive interference, as the source emit in opposite phases, the path difference between the distance to the person, measured in a straight line from the speakers, must be equal to an integer number of wavelengths.
We need to know the distance from the listener to the other speaker, located 4.4 m from the one which is directly in front of him, which we can find using Pythagorean theorem, as follows:
l₂ = √(3)²+(4.4)² = 5.33 m
The difference in path will be, then:
d = l₂-l₁ = 5.33 m - 3.00 m = 2.33 m
For the lowest frequency that gives destructive interference, the wavelength will be highest possible, which happens when the distance is just one wavelength.
⇒ d = λ = 2.33 m
In any wave, there exists a fixed relationship between speed, frequency and wavelength, as follows:
v = λ*f Κ ⇒ f = v/λ
Taking the speed of sound as 343 m/s, and solving for f, we get:
f= 343 m/s / 2.33 m = 147.21 Hz
