Question

During propagation of longitudinal plane wave in a medium, two particles separated by a distance equivalent to one wavelength at an instant will be/have
A. In phase, same displacement
B. In phase, displacement displacement
C. Different phase, same displacement
D. Different phase, different displacement

Answer 1

Hint: A wave is a disturbance that repeats itself after every interval of time. We can also say that a wave repeats itself every equal distance. This distance is called the wavelength of the wave. After every wavelength, the motion of the particles repeat.

Complete answer:
Let us first understand what a longitudinal wave is.
A wave is a disturbance caused in a medium. For example, ripples created when we throw a stone in water, vibrate a string of a guitar. The property of waves is that they can carry energy from one point to another.
A wave is formed due to the vibrations of the particles of the medium. When the motion or displacement of the particles are in the same direction in which the wave propagates, the wave is called a longitudinal wave.
A wave is a disturbance that repeats itself after every interval of time. We can also say that a wave repeats itself every equal distance. This distance is called the wavelength of the wave.
After every wavelength, the motion of the particles repeat. Therefore, if we consider two particles that are separated by a distance equal to the wavelength, their displacement will be the same and they will be in phase. Meaning they are moving in the same direction.

Hence, the correct option is A.

Note:
Remember that a separation of distance equal to integer multiples of wavelength is equivalent to a phase difference of integer multiples of $2\pi $ and we say that the particles are in phase.
If the separation is half of the wavelength of the wave then the phase difference between the two particles is $\pi $ and the magnitude of the displacement of the particles are the same but both are moving in opposite directions.