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What does the given equation: x = Asin(ky+wt+a) represent?
- a)Wave travelling along positive x direction
- b)Wave travelling along negative x direction
- c)Wave travelling along positive y direction
- d)Wave travelling along negative y direction
Correct answer is option 'D'. Can you explain this answer?
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What does the given equation: x = Asin(ky+wt+a) represent?a)Wave trave...
Wave representation
The given equation, x = Asin(ky wt a), represents a wave travelling along the negative y direction.
Explanation:
1. Equation breakdown:
- x: represents the displacement of the wave in the x-direction.
- A: represents the amplitude of the wave.
- sin(ky wt + a): represents the mathematical representation of the wave.
- k: represents the wave number, which is related to the wavelength of the wave.
- y: represents the displacement of the wave in the y-direction.
- wt: represents the angular frequency of the wave multiplied by time.
- a: represents the phase constant.
2. Wave travelling along the negative y direction:
- In the given equation, the displacement in the y-direction is represented by the term "ky".
- Since the coefficient of y is negative (-k), it indicates that the wave is travelling in the negative y direction.
3. Wave travelling along the negative x direction:
- In the given equation, the displacement in the x-direction is represented by the term "x".
- However, the equation does not contain any negative sign or coefficient related to x, indicating that the wave is not travelling along the negative x direction.
4. Wave travelling along the positive y direction:
- As mentioned earlier, the coefficient of y is negative (-k), which implies that the wave is not travelling along the positive y direction.
5. Wave travelling along the positive x direction:
- The given equation does not provide any information about the direction of the wave in the x-direction.
- Hence, it cannot be concluded that the wave is travelling along the positive x direction.
Thus, based on the analysis, the correct answer is option 'D' - the given equation represents a wave travelling along the negative y direction.
The given equation, x = Asin(ky wt a), represents a wave travelling along the negative y direction.
Explanation:
1. Equation breakdown:
- x: represents the displacement of the wave in the x-direction.
- A: represents the amplitude of the wave.
- sin(ky wt + a): represents the mathematical representation of the wave.
- k: represents the wave number, which is related to the wavelength of the wave.
- y: represents the displacement of the wave in the y-direction.
- wt: represents the angular frequency of the wave multiplied by time.
- a: represents the phase constant.
2. Wave travelling along the negative y direction:
- In the given equation, the displacement in the y-direction is represented by the term "ky".
- Since the coefficient of y is negative (-k), it indicates that the wave is travelling in the negative y direction.
3. Wave travelling along the negative x direction:
- In the given equation, the displacement in the x-direction is represented by the term "x".
- However, the equation does not contain any negative sign or coefficient related to x, indicating that the wave is not travelling along the negative x direction.
4. Wave travelling along the positive y direction:
- As mentioned earlier, the coefficient of y is negative (-k), which implies that the wave is not travelling along the positive y direction.
5. Wave travelling along the positive x direction:
- The given equation does not provide any information about the direction of the wave in the x-direction.
- Hence, it cannot be concluded that the wave is travelling along the positive x direction.
Thus, based on the analysis, the correct answer is option 'D' - the given equation represents a wave travelling along the negative y direction.
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Community Answer
What does the given equation: x = Asin(ky+wt+a) represent?a)Wave trave...
A way of looking at a travelling wave is considering the direction in which a particular value of transverse displacement moves. For the given equation x = Asin(ky+wt+a) we have to see the direction in which x moves. For eg: If we consider the amplitude A, for x =A as t increases, y should decrease. So, we can say that the wave propagates in the negative y direction.
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What does the given equation: x = Asin(ky+wt+a) represent?a)Wave travelling along positive x directionb)Wave travelling along negative x directionc)Wave travelling along positive y directiond)Wave travelling along negative y directionCorrect answer is option 'D'. Can you explain this answer?
Question Description
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