Answer:
(A) The wavelength of this wave is [tex]56\; \rm cm[/tex].
(B) The amplitude of this wave is [tex]6.5\; \rm cm[/tex].
Explanation:
Refer to the diagram attached. A point on this wave is at a crest or a trough if its distance from the equilibrium position is at a maximum.
The amplitude of a wave is the maximum displacement of each point from the equilibrium position. That's the same as the vertical distance between the crest (or the trough) and the equilibrium position.
- On the diagram, the distance between the two gray dashed lines is the vertical distance between a crest and a trough. According to the question, that distance is [tex]\rm 13\; \rm cm[/tex] for the wave in this rope.
- On the other hand, the distance between either gray dashed line and the black dashed line is the distance between a crest (or a trough) and the equilibrium position. That's the amplitude of this wave.
Therefore, the amplitude of the wave is exactly [tex]\displaystyle \frac{1}{2}[/tex] the vertical distance between a crest and a trough. Hence, for the wave in this question,
[tex]\begin{aligned}& \text{Amplitude}\\ &= \frac{1}{2} \times (\text{Vertical distance between crest and trough}) \\ &= \frac{1}{2} \times 13\;\rm cm = 6.5\; \rm cm\end{aligned}[/tex].
The wavelength of a transverse wave is the same as the minimum (horizontal) distance between two crests or two troughs. That's twice the horizontal distance between a crest and a trough in the same period.
[tex]\begin{aligned}& \text{Wavelength}\\ &= 2 \times (\text{Horizontal distance between adjacent crest and trough}) \\ &= 2 \times 28\;\rm cm = 56\; \rm cm\end{aligned}[/tex].
