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Two waves travel in the same direction along a string and interface. The waves have the same wavelength and travel with the same speed. The amplitude of each wave is 9.7 mm , and there is a phase difference of 110° between them. What is the amplitude of the combined wave resulting from the interface of the two waves ?
- a)11.1 mm
- b)21.2 mm
- c)27.3 mm
- d)30.7 mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two waves travel in the same direction along a string and interface. T...
The amplitude of the combined wave
2ym | cos(ΔØ/)/2)= 2(9.7mm) cos(110°/2)
= 11.1 mm
2ym | cos(ΔØ/)/2)= 2(9.7mm) cos(110°/2)
= 11.1 mm
Most Upvoted Answer
Two waves travel in the same direction along a string and interface. T...
Degrees between the two waves.
To find the resultant amplitude of the waves, we can use the formula for the sum of two waves with a phase difference:
Resultant amplitude = √(A1^2 + A2^2 + 2A1A2cosΦ)
Where A1 and A2 are the amplitudes of the two waves, and Φ is the phase difference.
Plugging in the values given:
Resultant amplitude = √((9.7 mm)^2 + (9.7 mm)^2 + 2 * 9.7 mm * 9.7 mm * cos(110°))
Resultant amplitude = √(94.09 mm^2 + 94.09 mm^2 + 2 * 9.7 mm * 9.7 mm * (-0.342))
Resultant amplitude = √(188.18 mm^2 + 59.52 mm^2)
Resultant amplitude = √(247.7 mm^2)
Resultant amplitude = 15.74 mm
Therefore, the resultant amplitude of the two waves is 15.74 mm.
To find the resultant amplitude of the waves, we can use the formula for the sum of two waves with a phase difference:
Resultant amplitude = √(A1^2 + A2^2 + 2A1A2cosΦ)
Where A1 and A2 are the amplitudes of the two waves, and Φ is the phase difference.
Plugging in the values given:
Resultant amplitude = √((9.7 mm)^2 + (9.7 mm)^2 + 2 * 9.7 mm * 9.7 mm * cos(110°))
Resultant amplitude = √(94.09 mm^2 + 94.09 mm^2 + 2 * 9.7 mm * 9.7 mm * (-0.342))
Resultant amplitude = √(188.18 mm^2 + 59.52 mm^2)
Resultant amplitude = √(247.7 mm^2)
Resultant amplitude = 15.74 mm
Therefore, the resultant amplitude of the two waves is 15.74 mm.
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Two waves travel in the same direction along a string and interface. The waves have the same wavelength and travel with the same speed. The amplitude of each wave is 9.7 mm , and there is a phase difference of 110° between them. What is the amplitude of the combined wave resulting from the interface of thetwo waves ?a)11.1 mmb)21.2 mmc)27.3 mmd)30.7 mmCorrect answer is option 'A'. Can you explain this answer?
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