Answer:
1089.74 Hz
Explanation:
Using Pythagoras theorem, we can find the distance from the point to the second speaker.
Thus;
d2 = √(3² + 2.3²)
d2 = √(9 + 5.29)
d2 = √14.29
d2 = 3.78 m
Then, the path distance which is the extra distance travelled would be;
Δd = d2 - d1
Δd = 3.78 - 3
Δd = 0.78 m
Now, the destructive interference condition is given by the formula;
Δd = (m + ½)λ
λ is the wavelength
m is a non - negative integer.
In this case, m = 2
Thus;
0.78 = (2 + ½)λ
λ = 0.78/(2½)
λ = 0.312 m
Now the formula for frequency of a wave is given by;
f = v/λ
Where v is speed of sound.
Thus;
f = 340/0.312
f = 1089.74 Hz
