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Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:
- a)4 : 1
- b)25 : 9
- c)16 : 9
- d)5 : 3
Correct answer is option 'B'. Can you explain this answer?
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Interference of Waves
When two coherent sources produce waves that overlap, interference occurs. Interference can be either constructive or destructive, depending on the phase difference between the waves.
Intensity of Waves
The intensity of a wave is defined as the power transported by the wave per unit area perpendicular to the direction of wave propagation. Mathematically, it is given by the equation:
Intensity (I) = Power (P) / Area (A)
Since intensity is directly proportional to the square of the amplitude of the wave, we can write:
I ∝ A^2
Maximum and Minimum Intensity
In the case of interference, the maximum intensity occurs when the waves are in phase and constructively interfere, while the minimum intensity occurs when the waves are completely out of phase and destructively interfere.
Let the maximum intensity be Imax and the minimum intensity be Imin. Given that the ratio of Imax to Imin is 16, we can write:
Imax / Imin = 16
Taking the square root of both sides, we have:
√(Imax / Imin) = √16
Imax / Imin = 4
Ratio of Intensities
The ratio of the intensities of the waves is equal to the square of the ratio of their amplitudes. Let the amplitudes of the waves be A1 and A2. We can write:
(I1 / I2) = (A1^2 / A2^2)
Since the ratio of Imax to Imin is 4, we can write:
Imax / Imin = (A1^2 / A2^2) = 4
Taking the square root of both sides, we have:
√(A1^2 / A2^2) = √4
A1 / A2 = 2
Therefore, the amplitudes of the waves are in the ratio of 2 : 1. Since intensity is directly proportional to the square of the amplitude, we square the ratio of amplitudes:
(A1 / A2)^2 = (2 / 1)^2 = 4
Hence, the intensity of the waves is in the ratio of 4 : 1.
Therefore, the correct answer is option 'A' (4 : 1).
When two coherent sources produce waves that overlap, interference occurs. Interference can be either constructive or destructive, depending on the phase difference between the waves.
Intensity of Waves
The intensity of a wave is defined as the power transported by the wave per unit area perpendicular to the direction of wave propagation. Mathematically, it is given by the equation:
Intensity (I) = Power (P) / Area (A)
Since intensity is directly proportional to the square of the amplitude of the wave, we can write:
I ∝ A^2
Maximum and Minimum Intensity
In the case of interference, the maximum intensity occurs when the waves are in phase and constructively interfere, while the minimum intensity occurs when the waves are completely out of phase and destructively interfere.
Let the maximum intensity be Imax and the minimum intensity be Imin. Given that the ratio of Imax to Imin is 16, we can write:
Imax / Imin = 16
Taking the square root of both sides, we have:
√(Imax / Imin) = √16
Imax / Imin = 4
Ratio of Intensities
The ratio of the intensities of the waves is equal to the square of the ratio of their amplitudes. Let the amplitudes of the waves be A1 and A2. We can write:
(I1 / I2) = (A1^2 / A2^2)
Since the ratio of Imax to Imin is 4, we can write:
Imax / Imin = (A1^2 / A2^2) = 4
Taking the square root of both sides, we have:
√(A1^2 / A2^2) = √4
A1 / A2 = 2
Therefore, the amplitudes of the waves are in the ratio of 2 : 1. Since intensity is directly proportional to the square of the amplitude, we square the ratio of amplitudes:
(A1 / A2)^2 = (2 / 1)^2 = 4
Hence, the intensity of the waves is in the ratio of 4 : 1.
Therefore, the correct answer is option 'A' (4 : 1).
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Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:a)4 : 1b)25 : 9c)16 : 9d)5 : 3Correct answer is option 'B'. Can you explain this answer?
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