/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 4 Sketch a sinusoidal wave with an... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 25: Problem 4

Sketch a sinusoidal wave with an amplitude of \(2 \mathrm{cm}\) and a wavelength of \(6 \mathrm{cm} .\) This wave represents the electric field portion of a visible EM wave traveling to the right with intensity \(I_{0}\). (a) Sketch an identical wave beneath the first. What is the amplitude (in centimeters) of the sum of these waves? (b) What is the intensity of the new wave? (c) Sketch two more coherent waves beneath the others, one of amplitude \(3 \mathrm{cm}\) and one of amplitude \(1 \mathrm{cm},\) so all four are in phase. What is the amplitude of the four waves added together? (d) What intensity results from adding the four waves?

Short Answer

Expert verified
Question: Given four coherent sinusoidal waves with amplitudes of 2 cm, 2 cm, 3 cm, and 1 cm, and a wavelength of 6 cm, find the intensity of the resulting wave when all four waves are added together. Answer: The intensity of the resulting wave when all four coherent sinusoidal waves are added together is 16I鈧�.

Step by step solution

01

Understanding the relationship between amplitude and intensity

The intensity (\(I\)) of a wave is directly proportional to the square of its amplitude (\(A\)). Mathematically, it is given by \(I \propto A^{2}\).
02

Amplitude of the sum of two identical sinusoidal waves

In part (a), we are asked to sketch two identical sinusoidal waves with amplitude 2 cm and wavelength 6 cm and find the amplitude of the sum of these two waves. Since they are identical and in phase, their amplitudes simply add up: \(A_{sum} = A_1 + A_2 = 2 + 2 = 4 \mathrm{cm}\).
03

Intensity of the new wave

In part (b), we find the intensity of the new wave formed after summing the two identical sinusoidal waves. Since intensity is proportional to the square of amplitude, the new intensity is: \(I_{new} = I_0 \left( \frac{A_{sum}}{A_1} \right)^2 = I_0 \left( \frac{4}{2} \right)^2 = 4 I_0\).
04

Adding more coherent waves

In part (c), we are adding two more coherent sinusoidal waves beneath the previous two waves, one with an amplitude of 3 cm and one with an amplitude of 1 cm, so that all waves are in phase. The total amplitude can be found as: \(A_{total} = A_{sum} + A_3 + A_4 = 4 + 3 + 1 = 8 \mathrm{cm}\).
05

Intensity of the resulting wave

In part (d), we need to find the intensity of the resulting wave when all four waves are added together. The resulting intensity can be calculated as: \(I_{result} = I_0 \left( \frac{A_{total}}{A_1} \right)^2 = I_0 \left( \frac{8}{2} \right)^2 = 16 I_0\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The first two dark fringes on one side of the central maximum in a single-slit diffraction pattern are \(1.0 \mathrm{mm}\) apart. The wavelength of the light is \(610 \mathrm{nm}\) and the screen is \(1.0 \mathrm{m}\) from the slit. What is the slit width?
Two slits separated by \(20.0 \mu \mathrm{m}\) are illuminated by light of wavelength \(0.50 \mu \mathrm{m} .\) If the screen is \(8.0 \mathrm{m}\) from the slits, what is the distance between the \(m=0\) and \(m=1\) bright fringes?
A double slit is illuminated with monochromatic light of wavelength $600.0 \mathrm{nm} .\( The \)m=0\( and \)m=1\( bright fringes are separated by \)3.0 \mathrm{mm}\( on a screen \)40.0 \mathrm{cm}$ away from the slits. What is the separation between the slits? [Hint: Is the small angle approximation justified?]

Young's Double-Slit Experiment Light of \(650 \mathrm{nm}\) is incident on two slits. A maximum is seen at an angle of \(4.10^{\circ}\) and a minimum of \(4.78^{\circ} .\) What is the order \(m\) of the maximum and what is the distance \(d\) between the slits?
Roger is in a ship offshore and listening to a baseball game on his radio. He notices that there is destructive interference when seaplanes from the nearby Coast Guard station are flying directly overhead at elevations of $780 \mathrm{m}, 975 \mathrm{m},\( and \)1170 \mathrm{m} .$ The broadcast station is \(102 \mathrm{km}\) away. Assume there is a \(180^{\circ}\) phase shift when the EM waves reflect from the seaplanes. What is the frequency of the broadcast?
See all solutions

Recommended explanations on Physics Textbooks

Particle Model of Matter

Read Explanation

Energy Physics

Read Explanation

Solid State Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Fluids

Read Explanation

Kinematics Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.