Consider two points lying at a distance of 10 m and 15 m from an oscillating source. If the pe

step 1 In this question, we will learn about some basic concept of the oscillation and waves. The quest

Consider two points lying at a distance of 10 m and 15 m...

Consider two points lying at a distance of $10 \mathrm{~m}$ and $15 \mathrm{~m}$ from an oscillating source. If the periodic time of oscillation is $0.05 \mathrm{~s}$ and the velocity of wave produced is $300 \mathrm{~m} / \mathrm{s}$, then what will be the phase difference the two points? (A) $\pi$ (B) $\pi / 6$ (C) $\pi / 3$ (D) $2 \pi / 3$

Consider two points lying at a distance of $10 \mathrm{~m}$ and $15 \mathrm{~m}$ from an oscillating source. If the periodic time of oscillation is $0.05 \mathrm{~s}$ and the velocity of wave produced is $300 \mathrm{~m} / \mathrm{s}$, then what will be the phase difference the two points?
(A) $\pi$
(B) $\pi / 6$
(C) $\pi / 3$
(D) $2 \pi / 3$

Key Concepts

Wave Properties

Wave properties refer to the fundamental characteristics of waves, including velocity, wavelength, period, frequency, and amplitude. These properties are interrelated; for example, the wavelength of a wave is given by the product of its velocity and period (or equivalently, the quotient of velocity divided by frequency). Understanding these basic properties is essential for analyzing how waves propagate and interact with different points in space.

Wavelength Calculation

Wavelength is a key concept in wave motion, defined as the spatial period of the wave—the distance over which the wave's shape repeats. It is calculated using the relation ? = vT, where v is the velocity of the wave and T is the period. This relation helps in connecting the temporal characteristic of a wave (period) with its spatial behavior.

Path Difference

Path difference is the difference in the distances traveled by two parts of a wave (or by the same wave reaching two different points from the same source). This difference in travel distances results in a phase difference between the waves observed at these points. Understanding path difference is crucial for analyzing interference and phase relations in wave phenomena.

Phase Difference

Phase difference quantifies how much one wave is shifted relative to another in its cycle, typically expressed in radians or degrees. It is directly related to the path difference by the formula ?? = (2?/?)?x, where ?x is the path difference and ? is the wavelength. This concept is pivotal in understanding how waves constructively or destructively interfere based on their relative displacements.

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