Question 279: Waves

Question

When the string is stretched between two rigid supports, under certain tension and vibrated

Accepted Answer

When a string is stretched between two rigid supports (fixed ends) and vibrated, the boundary conditions require that the displacement at the supports is zero. This means that the ends of the string must always be nodes (points of zero amplitude).
For the fundamental mode (the lowest frequency of vibration), the string forms a half-wave pattern with one antinode (point of maximum amplitude) in the middle. Mathematically, the condition for standing waves on a string fixed at both ends is given by:
$$L = \frac{n\lambda}{2}, \quad n = 1,2,3,\ldots$$
For $n=1$, this implies that:
$$L = \frac{\lambda}{2},$$
which corresponds to one half-wavelength along the length of the string. Consequently, there are nodes at both ends and one antinode in the center.
Thus, the correct answer is:
Ã¢ÂÂ¢ Option B: Nodes at both ends and at least one antinode in between.

Answer

antinodes at both ends and at least one node in between

Answer

Nodes at both ends and at least one antinode in between

Answer

Nodes at both ends and no antinode in between

Answer

antinodes at both ends and no node in between

Waves

When the string is stretched between two rigid supports, under certain tension and vibrated

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