Respuesta :
Answer:
Condition of constructive interference is given as
x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm
condition of destructive interference we know that
x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm
Explanation:
As we know that the frequency of the sound waves is 1100 Hz
now we can find the wavelength as
[tex]\lambda = \frac{c}{f}[/tex]
now we have
[tex]\lambda = \frac{330}{1100}[/tex]
[tex]\lambda = 30 cm[/tex]
now we know for the condition of constructive interference
Path difference = N[tex]\lambda[/tex]
[tex](1 - x) - x = N(0.30)[/tex]
[tex]1 - 2x = N(0.30)[/tex]
[tex]x = \frac{1 - 0.30 N}{2}[/tex]
x = 95 cm, 80 cm, 65 cm, 50 cm, 35 cm, 20 cm, 5 cm
Similarly for condition of destructive interference we know that
Path difference = (2N + 1)[tex]\frac{\lambda}{2}[/tex]
so we have
[tex](1 - x) - x = (2N + 1)(0.15)[/tex]
[tex]1 - 2x = N(0.30) + 0.15[/tex]
[tex]x = \frac{0.85 - 0.30 N}{2}[/tex]
x = 87.5 cm, 72.5 cm, 57.5 cm, 42.5 cm, 27.5 cm, 12.5 cm
The points on a line between speakers where there will be destructive interference is; 0.172 m
How to find constructive and destructive interference?
From wave equations, we know that;
Wavelength;λ = f/v
Where v is speed of sound in air with a constant value of 344 m/s
Frequency; f = 1000 Hz
λ = v/f
λ = 344/1000
λ = 0.344 m
Constructive interference will occur when the two waves differ by a distance of nλ and when they have the same wavelength.
At constructive interference point, my distance from both speakers will be x.
Since the distance between speaker A and B is 1 m, then;
difference in path is;
nλ = 1 - x - x
nλ = 1 - 2x
Making x the subject, gives;
x = 1/2 - nλ/2
Plugging in 0.344 for λ gives;
x = 1/2 - n(0.344)/2
x = 1/2 - 0.172n
So, since it's at point 1, we'll label it accordingly.
Thus;
x_1 = 0.5 - 0.172(n_1)
Now, we know that destructive interference will occur when the two waves differ by a distance of; (½ + n)λ and when they have the same wavelength.
Thus,
1 - 2x = (½ + n)λ
Plugging in 0.344 for λ to give;
1 - 2x = 0.086 + 0.344n
x = 0.457 - 0.172n
Since second point, then;
x2 = 0.457 - 0.172(n_2)
To find out how far I must walk toward speaker B to move to a point of destructive interference, it will be;
x1 - x2 which gives;
0.5 - 0.172(n_1) - 0.457 - 0.172(n_2)
This gives;
0.043 - (0.172(n_1) - 0.172(n_2))
This means that 0.172 m is the distance since I have to subtract difference of 0.172 multiplied by the difference of n_1 and n_2 from 0.043.
Read more about Interference at; https://brainly.com/question/17581578
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