waves sketching

The travelling wave is sinusoidal in form, hence you could first sketch out the displacement-distance graph of the wave at t = 0, based on the given figure.

Since from the given figure, the particle at x = 0 will be going up as time progresses. The displacement-distance graph of the wave will then be an "inverted sine-wave). That is, the displacement is -ve from x = 0 to x = 入/2 (入 is the wavelength) and the displacement is +ve from x = 入/2 to x = 入.

Now, the nearest point with zero displacement is the one at 入/2, and is given to be 5 cm away. From this information, we know that 入/2 = 5 cm, hence the wavelength 入 = 2x 5 cm = 10 cm.

Here, you could complete the displacement-distance graph, which is an "inverted sine wave" with a wavelength of 10 cm

The period of the wave can be found from the given figure, as it takes 0.4 s for the particle at x=0 to complete one cycle, the period is thus 0.4 s.

The question then asks what is the waveform after 0.1 s, i.e. 1/4 of a period. During 1/4 period, all particles displace 1/4 of a cycle. In other words, the sketched displacement-distance graph will shift a distance of 入/4 towards the right. Thus, particle at x will be at the highest point (+4 cm from the mean position), the particle at x = 5 cm will displace to the lowest point (-4 cm from the mean position). The particle at 10 cm, which behaves like the one at x = 0, will be at +4 cm. This is the graph given in the answer.

wavelength=5cm
t=0.1s
a=4cm

upper graph: when t=0.1s,
s=+4cm(x=0---> beginning pt.)
lower graph -->at t=0.1s
start with +4cm(beginning pt.)
wavelength=10cm
from 0cm-10cm> 1 wave