Half a wavelength must fit exactly into the length of a vibrating cord
Explanation:
A standing wave is a wave produced by the interference between a wave and its reflection. A standing wave is the wave produced, for instance, in the string of a guitar.
A standing wave is different from other types of waves because it does not propagate in space, but it only vibrate in a fixed region.
A standing wave is characterized by the presence of:
- Nodes: points where the amplitude of the wave is always zero (destructive interference)
- Antinodes: points where the amplitude of the wave is maximum (constructive interference)
The two ends of the string do not vibrate: this means that they always correspond to two nodes. If we take the fundamental mode of vibration of the string (so, no other nodes), we see that the length of the string corresponds to the distance between two consecutive nodes: however, this also corresponds to half the wavelength of the wave. Therefore, we can conclude that the correct option is
Half a wavelength must fit exactly into the length of a vibrating cord
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