two possible wavelength of this wave?

Question

a transverse wave travels along horizontal stretched string.in front of string is a screen with two slots in it so that all an observer can see is the motion of two points in string placed 3m apart.the observer notes that two points perform SHM with a period of 2s and that one points lags in phase difference by 90 degree compared w other.calculate (A)the frequency of wave(b)two possible values for the wavelength of wave
i have done part one whose answer is0.50hz but could not solve its second part whose answers are 12m and 2.4m
plz do it for me

Answer 1

You already got a. Very good.

Next, remember, the phase shift is proportional to the distance, and the phase shift over an entire wavelength is 360 degrees.

So if the phase shift over 3 meters is 90 degrees, then the wavelength is equal to 3 meters times 360 degrees over 90 degrees. This is 12 m.

But the phase shift could also be 90 degrees plus 360 degrees (450 degrees) and you'd see the same thing.

So the wavelength could be 3 meters times 360 degrees over 450 degrees. This is 2.4 meters

But the phase shift could also be 90 degrees plus 720 degrees (810 degrees) and you'd see the same thing.

So the wavelength could be 3m times 360/810 = whatever.

You can keep going like that.

Make sense?