Question

The phase difference between a particle at compression and a particle at the next rarefaction is:
A) $Zero$
B) $2 \pi$​
C) $\pi$
D) $\dfrac{\pi }{4}$

Answer 1

Hint: The phase difference is defined as the angular phase between the maximum possible value of the two alternating quantities which are having the same frequency. The angle of phase differences is defined as the angle between zero points of the two alternating quantities.

Complete solution:
The phase difference between the two particles or between the two waves indicates how much a particle or a wave is in front or behind another particle or the wave.
Phase difference value ranges from $0$ to 2$\pi $radians.
We know that the phase difference between the two successive compressions of rarefaction is 2$\pi $. As rarefaction appears between the two compressions, the phase difference is $\pi $.

Hence the correct option is C.

Note: 1) Compression is defined as the region in a longitudinal wave where the particles are closer together. In other words, it is the region where the medium is compressed. Rarefaction is defined as the region in a longitudinal wave where the particles are farthest apart. In other words, it is the region where the medium is spread out.
2) Waves are made up of compressions and rarefactions. Compressions are formed when molecules are forced together. Rarefactions are formed when molecules are given extra space and allowed to expand.
3) Compressions and rarefactions travel in the same direction at the same speed. The distance between two consecutive compressions and rarefactions in a wave is called the wavelength.
4) The distance between compression and the next rarefaction of a longitudinal wave is $\dfrac{1}{2}$ of wavelength.