A stretched wire resonates in one loop. The midpoint of the wire oscillates with an amplitude of A. What is the traveled distance of the midpoint in one period?

Please help me understand this relationship. Thank you very much!

If the amplitude is A, then it goes from -A to +A, or a distance of 2A. But during one period, it goes up and back again, for a distance of 4A.

To find the traveled distance of the midpoint in one period, we need to understand the relationship between the amplitude and the wavelength of the wave on the stretched wire.

In a standing wave formed on a stretched wire, the nodes (points of no displacement) are formed at the ends of the wire, while the antinodes (points of maximum displacement) are formed at the midpoint and at regular intervals along the wire.

Since the midpoint of the wire is an antinode, its maximum displacement is equal to the amplitude (A). The traveled distance of the midpoint in one period is twice the distance between adjacent antinodes.

The distance between adjacent antinodes is equal to half the wavelength (λ/2) of the wave.

Therefore, the traveled distance of the midpoint in one period is given by:

Traveled distance = 2 * (λ/2) = λ

Where λ is the wavelength of the wave.

So, in summary, the traveled distance of the midpoint in one period is equal to the wavelength (λ) of the wave on the stretched wire.

To find the traveled distance of the midpoint in one period, we need to understand the relationship between the frequency of oscillation and the wavelength of the wave on a stretched wire.

When a wire is stretched and resonates in one loop, it forms a standing wave. In a standing wave, certain points along the wave remain fixed, called nodes, while other points oscillate with a maximum amplitude, called antinodes.

In this case, the midpoint of the wire oscillates with an amplitude of A. This means that the midpoint is an antinode, which is a point that experiences maximum displacement in a standing wave.

In one complete period of oscillation, the midpoint moves back and forth from its maximum displacement on one side to its maximum displacement on the other side. This means that it travels a distance equal to twice the amplitude, which is 2A.

Therefore, the traveled distance of the midpoint in one period is 2A.