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A string of length 2 m is fixed at both the ends. The string is vibrating in the second harmonics and the amplitude of the antinode is 4 mm. What will be the amplitude of a particle in the string situated at a distance of 0.25 m from one of the fixed ends?
  • a)
    2√2 mm
  • b)
    2 mm
  • c)
    2/√2
  • d)
    √2 mm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A string of length 2 m is fixed at both the ends. The string is vibrat...
The equation of the standing wave is given by:

And the amplitude of the particle at a distance x from the fixed end is given by
A = 2a sin (kx)
Since the string is vibrating in second harmonics, so there will be two loops in the string.
Therefore,

Amplitude at the anti-node = 4 mm
Therefore, 2a = 4 mm
Thus, amplitude of particle 
This is our required solution.
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Community Answer
A string of length 2 m is fixed at both the ends. The string is vibrat...
In a string fixed at both ends and vibrating in the second harmonic, the length of the string is equal to half the wavelength of the wave. Since the length of the string is 2 m, the wavelength of the wave is 4 m.

The distance from one fixed end to the particle is 0.25 m. This distance is equal to one-eighth of the wavelength.

The amplitude of a particle in a wave decreases as the distance from the antinode increases. In this case, the distance from the particle to the antinode is four times the distance from the antinode to the fixed end.

Therefore, the amplitude of the particle will be one-fourth of the amplitude of the antinode.

Amplitude of the particle = 1/4 * 4 mm = 1 mm

Therefore, the amplitude of the particle situated at a distance of 0.25 m from one of the fixed ends is 1 mm.
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A string of length 2 m is fixed at both the ends. The string is vibrating in the second harmonics and the amplitude of the antinode is 4 mm. What will be the amplitude of a particle in the string situated at a distance of 0.25 m from one of the fixed ends?a)2√2 mmb)2 mmc)2/√2d)√2 mmCorrect answer is option 'A'. Can you explain this answer?
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