Physics - Wave on String Question with Solution | TestHub

Two points on a progressive wave are in the same state of vibration (in phase) if they have the same displacement from the mean position and are moving in the same direction.

This condition is met when the points are separated by a distance of $n\lambda$, where $n$ is an integer and $\lambda$ is the wavelength. On the waveform, such points will have the same displacement $y$ and the same slope.

From the given wave diagram:

Point B is on the falling edge of the first positive half-cycle (displacement $y>0$, slope is negative).

Point E is on the falling edge of the third positive half-cycle (displacement $y>0$, slope is negative).

Both points B and E have the same displacement and the same slope, indicating they are in the same phase. They are separated by exactly two full wavelengths ($2\lambda$).

Therefore, points B and E are in the same state of vibration.

Answer: E, B