Two coherent waves with intensities 9 I and 16 I are reaching a point with phase difference zero

Name: Problem 159, Chapter 1: IIT JEE Super Course in Physics: Optics and Modern Physics
Uploaded: 2021-06-14T08:38:09-08:00
Duration: 1 min 21 s
Channel: Ajay Singhal
Description: Two coherent waves with intensities 9 I and 16 I are reaching a point with phase difference zero. At the point of interference, the intensity is (a) 7 I (b) 25 I (c) 36 I (d) 49 I

step 1 So in this question, we have two coherent waves with intensities i1 equals to 9i and i2. This is

Question

Two coherent waves with intensities $9 \mathrm{I}$ and $16 \mathrm{I}$ are reaching a point with phase difference zero. At the point of interference, the intensity is (a) $7 \mathrm{I}$ (b) $25 I$ (c) $36 \mathrm{I}$ (d) $49 \mathrm{I}$

   Two coherent waves with intensities $9 \mathrm{I}$ and $16 \mathrm{I}$ are reaching a point with phase difference zero. At the point of interference, the intensity is
(a) $7 \mathrm{I}$
(b) $25 I$
(c) $36 \mathrm{I}$
(d) $49 \mathrm{I}$

IIT JEE Super Course in Physics: Optics and Modern Physics

Trishna Knowledge… 1st Edition

Chapter 1, Problem 159

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Solved by Expert Ajay Singhal

06/14/2021

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We need to find the intensity at the point of interference. Show more…

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Two coherent waves with intensities $9 \mathrm{I}$ and $16 \mathrm{I}$ are reaching a point with phase difference zero. At the point of interference, the intensity is (a) $7 \mathrm{I}$ (b) $25 I$ (c) $36 \mathrm{I}$ (d) $49 \mathrm{I}$

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Key Concepts

Intensity and Amplitude Relationship

In wave physics, the intensity of a wave is proportional to the square of its amplitude. This means when given intensities, extracting the amplitudes requires taking the square root of the intensity values. This principle is essential when combining wave amplitudes to determine the resulting intensity.

Constructive Interference

When two coherent waves combine with a zero phase difference, they undergo constructive interference. This causes their amplitudes to add directly, resulting in a total amplitude equal to the sum of the individual amplitudes. The overall intensity is then calculated by squaring this total amplitude.

Coherence

Coherence refers to the constant phase relationship between waves. It is a prerequisite for stable interference effects, such as constructive or destructive interference, and ensures that the added amplitudes yield consistent interference patterns.

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