Location of point mass based on graphs

[songoku]

Homework Statement

A simple harmonic transverse wave is travelling in the medium along negative x-direction. The waveform at t=1 s is shown in Figure a. The time dependence of displacement of a point mass in the medium is shown in Figure b. This point mass may be located at...
A) x = 0 m
B) x = 1 m
C) x = 2 m
D) x = 3 m

Relevant Equations

Not sure

Since figure (a) shows the waveform at t = 1 s, I also look at figure (b) when t = 1 s. The value of y is zero so I try to find the location of x from figure (a) for which y = 0. There are two value of x, 0 and 2 m.

Let say x = 0 is point P and x = 2 m is point Q. The period is 4 s so at t = 1 s, the wave has travelled to left for a quarter wave so initially point P is at x = 1 m and point Q is at x = 3 m so I think the answer is either B or D but I don't know how to determine which one is correct.

Thanks

 

[vela]

You're mistaking the point of constant phase on the wave with the location of the point mass. The point mass moves vertically; it doesn't move along the direction of propagation of the wave.

 

[Lnewqban]

... Since figure (a) shows the waveform at t = 1 s, I also look at figure (b) when t = 1 s. The value of y is zero so I try to find the location of x from figure (a) for which y = 0. There are two value of x, 0 and 2 m.

It is also important to consider either the point is moving upwards or downwards at t=1 s.
Imagine a paper ship floating on a lake, staying at same place, while riding (up and down) a wave caused by a stone falling nearby.

 

[songoku]

You're mistaking the point of constant phase on the wave with the location of the point mass. The point mass moves vertically; it doesn't move along the direction of propagation of the wave.

Ah yes

It is also important to consider either the point is moving upwards or downwards at t=1 s.
Imagine a paper ship floating on a lake, staying at same place, while riding (up and down) a wave caused by a stone falling nearby.

I think I get it. At t = 1 s, the mass is moving downwards so the answer should be x = 0 since x = 2 m is moving upwards.

Thank you very much for the help and explanation vela and Lnewqban