Explanation 1) Concept: We can use the concept of the vector addition law. The intensity is proportional to the square pf the resultant amplitude field. Consider the given waves as a vector and add their x components and y components separately. Find out the magnitude of the resultant and the angle by using the vector addition concept. 2) Formula: i) y R → = y h → + y v → ii) β = tan - 1 ⁡ y v y h iii) y = y 1 + y 2 iv) y = y R sin ⁡ ω t + β 3) Given: i) y 10 = 1.0 ii) y 20 = 2.0 iii) ∅ = 60 ° 4) Calculations: The phasor diagram for the given quantities is We choose t = 0 , for which the phasors representing the two waves are shown in the figure. We can add these two phasors by the vector components method. Let the two waves are y 1 = y 10 sin ⁡ ω t y 2 = y 20 sin ⁡ ω t + ∅ By putting the given values as y 1 = 1.0 sin ⁡ ω t y 20 = 2.0 sin ⁡ ω t + 60 ° y = y 1 + y 2 The sum of their horizontal components is ∑ y h = y 1 x + y 2 x ∑ y h = 1

11th Edition

ISBN: 9781119459170

Author: Halliday

Publisher: WILEY

See similar textbooks

Concept explainers

Electromagnetic Waves

Electromagnetic waves are waves that consist of magnetic field and electric field components perpendicular to each other. These field components are also perpendicular to the direction of propagation of the wave.

Question

Chapter 35, Problem 29P

To determine

To find:

The resultant of the amplitude.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 35, Problem 28P

Chapter 35, Problem 30P

Students have asked these similar questions

Draw a right-handed 3D Cartesian coordinate system (= x, y and z axes). Show a vector A with tail in the origin and sticking out in the positive x, y and z directions. Show the angles between A and the positive x, y and z axes, and call these angles α₁, α₂ and α3 Prove that Ax Acos α₁ Ay = Acos α₂ A₂- Acos α3

solve for Vo

Draw a third quadrant vector C. (remember that boldface characters represent vector quantities). Show the standard angle 0 for this vector (= angle that C makes with the positive x- axis). Also show the angle that C makes with the negative y-axis: call the latter angle 8. Finally, show the smallest angles that C makes with the positive x-axis and the positive y-axis: call these angles p1 and p2, repectively. a) Prove the following formulas for the components of C involving the standard angle (hint: start with the formulas for the components based on the angle & and then use (look up if necessary) co-function identities linking cosine and sine of 8 to sine and cosine of 0 since 8 = 3π/2-8 (this will switch cosine and sine around and eliminate - signs as well)) - C=Ccose C₁=Csine b) Prove the following formulas for the components of C: C=Ccosp1 C=Ccosp2

Chapter 35 Solutions

FUND.OF PHYSICS(LL)-PRINT COMP-W/ACCESS

Ch. 35 - Does the spacing between fringes in a two-slit...Ch. 35 - a If you move from one bright fringe in a two-slit...Ch. 35 - Figure 35-22 shows two light rays that are...Ch. 35 - In Fig. 35-23, three pulses of lighta, b, and cof...Ch. 35 - Is there an interference maximum, a minimum, an...Ch. 35 - Figure 35-24a gives intensity I verus position x...Ch. 35 - Figure 35-25 shows two sources S1 and S2 that emit...Ch. 35 - Figure 35-26 shows two rays of light, of...Ch. 35 - Light travels along the length of a 1500-nm-long...Ch. 35 - Figure 35-27a shows the cross section of a...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The resultant of the amplitude.

Solution Summary: The author explains how to find the resultant of the amplitude by using the vector addition law.

Concept explainers

To find: The resultant of the amplitude.

Want to see the full answer?

Chapter 35 Solutions

To find:

The resultant of the amplitude.