When two sound waves having amplitude A, angular frequency ωand a phase difference of π/ 2 super

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

When two sound waves having amplitude A, angular frequency...

When two sound waves having amplitude A, angular frequency $\omega$ and a phase difference of $\pi / 2$ superposes, the maximum amplitude and angular frequency of the resultant wave is $\ldots \ldots \ldots \ldots$ (A) $\sqrt{2} \mathrm{~A}, \omega$ (B) $(\mathrm{A} / \sqrt{2}),(\omega / 2)$ (C) $(\mathrm{A} / \sqrt{2}), \omega$ (D) $\sqrt{2} \mathrm{~A},(\omega / 2)$

When two sound waves having amplitude A, angular frequency $\omega$ and a phase difference of $\pi / 2$ superposes, the maximum amplitude and angular frequency of the resultant wave is $\ldots \ldots \ldots \ldots$
(A) $\sqrt{2} \mathrm{~A}, \omega$
(B) $(\mathrm{A} / \sqrt{2}),(\omega / 2)$
(C) $(\mathrm{A} / \sqrt{2}), \omega$
(D) $\sqrt{2} \mathrm{~A},(\omega / 2)$

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Key Concepts

Superposition Principle

This concept states that when two or more waves overlap, their displacements add algebraically. The result is a superposed wave whose displacement at any point is the sum of the displacements of the individual waves, allowing for the analysis of interference and resultant amplitude.

Phase Difference

Phase difference is the measure of the separation between the phases of two oscillating waves. It critically determines the type of interference – constructive or destructive – when waves overlap, and governs how their amplitudes combine.

Resultant Amplitude

The resultant amplitude is obtained by the vector addition of the individual amplitudes adjusted for phase differences. In cases with a phase difference like ?/2, the amplitudes combine in quadrature, leading to a maximum amplitude that is different from a simple arithmetic sum.

Angular Frequency

Angular frequency describes how rapidly a wave oscillates in time and is directly related to the frequency of the wave. When waves superpose, if they share the same angular frequency, the resultant wave oscillates at that same angular frequency.

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