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DC Pandey Superposition of Waves Solutions

DC Pandey Waves and Thermodynamics Solutions for Chapter 15 ‘Superposition of Waves’ will help you in understanding how the incident and reflected rays overlap in a medium. In this chapter of DC Pandey Solutions, you will be introduced to the principle of superposition and interference of waves, reflection and transmission of waves, standing waves, normal modes in a string, and resonance. You will also learn about the physical quantities associated with waves such as speed, frequency, time period, wavelength, amplitude, intensity and phase. 

In this chapter, you will get to practice 84 questions divided into two exercises of JEE Main and JEE advanced systematically. You will get to solve questions of a wide variety of both subjective and objective type. All the patterns of questions asked in the competitive exams are covered in detail in this chapter including the assertion-reasoning, multiple-choice questions, match the columns, fill in the blanks, and long-answer type numerical questions. The exercise consists mainly of the advanced level complex problems. Practising these questions will help you in preparing for all the entrance exams such as BITSAT or JEE with complete conceptual clarity.

The Instasolv platform will assist you in solving the questions in the DC Pandey Superimposition of Waves effortlessly. The answers by our physics experts are written in such a manner that you will find appropriate reasoning in each step of all the answers. We use the simplest possible methods to solve the exercise questions to guide you in developing a strong foundation in waves and thermodynamics. Your consistency summed up with the team-work at the Instasolv platform will yield you good ranks in the entrance exams of your choice.

Important Topics for DC Pandey Waves and Thermodynamics Solutions Chapter 15: Superposition of Waves

Introduction

The phenomenon like the appearance of different colours in soap bubbles or young’s double-slit experiment can be explained using the principle of superposition. The waves that are incident on a surface and reflect often overlap leading to some special characteristics which we will study in this chapter.

Principle of Superposition

The principle of superposition describes the displacement of a particle in a medium when two or more waves traverse in a medium simultaneously without affecting the motion of one another. The resultant displacement of the particle is the vector sum of displacement produced by each wave individually and is given as,

Where yj =individual wave function

y(x,t)=resultant behaviour of medium as a product of position and time

This principle of superposition is applicable on all types of waves such as mechanical waves or electromagnetic waves. 

Interference of Waves

We have studied previously that square of Amplitude is directly proportional to Intensity by the equation 

Also, when there are two sine waves of equal angular velocity ω with a phase difference of φ then the amplitude is given as,

Now, if we assume that ρ, ω and v is equal for the interfering waves under consideration, then for constructive interference Cosφ=+1, hence

For destructive interference cosφ=-1, hence

Reflection and Transmission of a Wave

If the speed of a wave is more in a medium, then it is a rarer medium while if the speed of the wave decreases in a medium, it is a denser medium. A medium can be denser for one type of wave while it can be rarer for another type of wave. The laws of reflection and refraction remain unchanged. Following changes occur during reflection and refraction of waves in their physical properties:

  • Speed (v): In reflection, the speed of the wave remains unchanged while in refraction, speed varies according to the density of the medium.
  • Frequency (f), time period (T), and angular frequency (ω): All of these remain unchanged and can be evaluated by,

  • Wavelength (λ) and Wave Number (k): In reflection, both remain unchanged, while in transmission, wavelength and wavenumber change with the change in the medium.
  • Amplitude (A) and Intensity (I): Both these physical properties change in reflection as well as transmission unless it is a case of complete transmission or complete reflection.
  • Phase): No phase change occurs in transmission and reflection from a rarer medium whereas there is a phase change of when the wave is reflected from a denser medium.

Standing Waves

If we assume 2 harmonic waves with the same frequency and amplitude and apply the principle of superposition on them, we will get the equation for a standing wave as

Normal Modes of a String and Resonance

Strings that are fixed on both ends experience standing waves of specified wavelength only which are called normal modes. Resonance occurs when because of one vibrating another medium starts vibration with larger amplitude at a particular frequency. 

Exercise Discussion for DC Pandey Waves and Thermodynamics Solutions Chapter 15: Superposition of Waves

Exercise for JEE Main:

  • There are 21 subjective questions in which you will be required to find the amplitude, velocity, wavelengths, frequency in some particular overtones.
  • Questions 1-6 are based on the principle of superposition and the vector sum of the displacement of medium particles.
  • Questions 7-21 are about the standing waves and normal modes of a string.
  • There are 37 objective multiple-choice questions in this exercise including all the topics along with questions about resonance.

Exercise for JEE Advance:

  • Questions 1-10 in this exercise are assertion-reasoning questions covering the principle of superposition, changes in the physical properties of waves resonance, standing waves, etc.   
  • You will get to solve 5 match the columns questions with the 11 high-level subjective questions in this exercise

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