Question

Phase difference between a compression and its successful rare fraction is 2π radians.
(A) True
(B) False

Answer 1

Hint: Phase difference is the difference in radians or degrees when two or more waves reach their maximum or minimum values. Vibrating particles attain the same state of vibration or same state of phase after a time interval equal to the time period (T).

Complete step by step answer:
We are given to find whether the phase difference between a compression and its successful rare fraction is 2π radians or not.Two consecutive compressions will be in the same phase. The phase difference between two consecutive compressions is 2π.This implies that the phase difference between a compression and a consecutive rare faction is π.
To understand phase difference, let us consider two pendulums, which are set into oscillation from the same extreme point, such that they reach the mean position at the same time, and hence also reach the other extreme point, a same time interval aftermath.Therefore these two pendulums are said to be in phase.
Now, let us consider one pendulum dropped from extreme position & another pendulum starts moving at mean position, at same time. In this case we say that the phase difference between the two pendulums is π/2. If one of the pendulums is at one of the extremes and the other pendulum is at the opposite extreme, then the phase difference between these two pendulums is π. If both pendulums are initially at mean position and are heading towards opposite extremes, then the phase difference between these two pendulums will be 3π/2.
If a wave forms compression at time t =0 then after time T (time period) again a consecutive compression is produced with a phase difference of 2π. If a wave forms compression at time
t =0 then after time T/2, a rarefaction will be formed with a phase difference of π radians.
Therefore, the phase difference between a compression and its successful rare fraction is π radians not 2π radians.
The correct option is B i.e, False.

Note:The region of the longitudinal wave where the medium is compressed is called compression and the region where the medium is expanded is called rare fraction. Do not confuse a rare fraction with a compression.