Answer:
170 Hz
Explanation:
The path difference between two waves are given by:
Δ=[tex]\sqrt{12^2 +5^2 }[/tex] - 12
Δ = 1 m
In order to hear minimum intensity, the path difference will be
Δ = λ/2
λ = 2Δ
Also, We know that
V= f λ
λ=V/f
Therefore,
340/f = 2 x 1
f= 170 Hz
Thus, the frequency of the sound is 170 Hz
Answer:
The frequency of the sound is 170 Hz
Explanation:
Traveling wave is given as;
[tex]D(r,t) = D_o(r)sin(kr- \omega t + \phi_o)[/tex]
where;
r is the distance from the source
[tex](kr- \omega t + \phi_o)[/tex] is phase
Then phase difference is given as;
[tex]\delta \phi = 2 \pi\frac{\delta r}{\lambda} +\delta \phi_o[/tex]
The phase difference between the two speakers at maximum intensity;
[tex]\delta \phi = 2\pi \frac{\delta r}{\lambda}[/tex]
where;
λ is the wavelength
Δr is difference in distance between the two speakers
Δr = r₂ - r₁ = [tex]\sqrt{L^2 + d^2} -L[/tex]
Given;
distance between the two speakers, d = 5.0 m
distance to the plane of the speakers, L = 12.0 m
Δr = [tex]\sqrt{12^2 + 5^2} -12 = 1 \ m[/tex]
[tex]\delta \phi = 2\pi\frac{\delta r}{\lambda}[/tex]
[tex]\delta r = \frac{\delta \phi}{2\pi}\lambda[/tex], at minimum sound intensity, ΔФ = π
[tex]\delta r = \frac{\pi}{2\pi} \lambda\\\\\delta r = \frac{\lambda}{2}[/tex]
λ = 2Δr
λ = 2 (1) = 2m
[tex]f = \frac{v}{\lambda} = \frac{340}{2} = 170\ Hz[/tex]
Therefore, the frequency of the sound is 170 Hz
