Physics
Physics
5th Edition
ISBN: 9781260487008
Author: GIAMBATTISTA, Alan
Publisher: MCGRAW-HILL HIGHER EDUCATION
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 11, Problem 57P

(a)

To determine

The intensity of sound when the waves interfere constructively.

(a)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound when the waves interfere constructively is 0.25W/m2_.

Explanation of Solution

Given that the individual intensities of the waves are 0.040W/m2, and 0.090W/m2.

The intensity of the wave is directly proportional to the square of its amplitude.

Let A1 and A2 be the amplitudes of the two waves and I1 and I2 be their respective intensities.

Write the expression for the ratio of the amplitudes of the two waves.

A1A2=I1I2 (I)

Solve equation (I) for A1.

A1=A2I1I2 (II)

Write the expression of the amplitude A of the resultant wave after constructive interference.

A=A1+A2 (III)

Use equation (II) in (III).

A=A2I1I2+A2=A2(I1I2+1) (IV)

Let I be the resultant intensity after constructive interference.

Write the expression for the ratio of the amplitudes of the resultant wave and the wave with amplitude A.

AA2=II2 (V)

Use equation (IV) in (V) and solve for I.

A2(I1I2+1)A2=II2I=I2(I1I2+1)2 (VI)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (VI) to find I.

I=(0.090W/m2)(0.040W/m20.090W/m2+1)2=0.25W/m2

Therefore, the intensity of sound when the waves interfere constructively is 0.25W/m2_.

(b)

To determine

The intensity of sound when the waves interfere destructively.

(b)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound when the waves interfere destructively is 0.010W/m2_.

Explanation of Solution

Write the expression of the amplitude A of the resultant wave after destructive interference.

A=|A1A2| (VII)

Use equation (II) in (VII).

A=|A2I1I2A2|=|A2(I1I21)| (VIII)

Use equation (VIII) in (V) and solve for I.

|A2(I1I21)|A2=II2I=I2|I1I21|2 (IX)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (IX) to find I.

I=(0.090W/m2)|0.040W/m20.090W/m21|2=0.01W/m2

Therefore, the intensity of sound when the waves interfere destructively is 0.010W/m2_.

(c)

To determine

The intensity of sound after interference if the waves are incoherent.

(c)

Expert Solution
Check Mark

Answer to Problem 57P

The intensity of sound after interference if the waves are incoherent is 0.130W/m2_.

Explanation of Solution

Write the expression for the resultant intensity when the incoherent waves interfere.

I=I1+I2 (X)

Conclusion:

Substitute 0.040W/m2 for I1 and 0.090W/m2 for I2 in equation (X) to find I.

I=0.040W/m2+0.090W/m2=0.130W/m2

Therefore, the intensity of sound after interference if the waves are incoherent is 0.130W/m2_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 11 Solutions

Physics

Ch. 11.9 - Prob. 11.9CPCh. 11.10 - Prob. 11.10CPCh. 11.10 - Prob. 11.7PPCh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - Prob. 10CQCh. 11 - Prob. 11CQCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 1PCh. 11 - Prob. 2PCh. 11 - Prob. 3PCh. 11 - Prob. 4PCh. 11 - 5. At what rate does the jet airplane in Problem 4...Ch. 11 - Prob. 6PCh. 11 - Prob. 7PCh. 11 - Prob. 8PCh. 11 - Prob. 9PCh. 11 - Prob. 10PCh. 11 - 11. A metal guitar string has a linear mass...Ch. 11 - Prob. 12PCh. 11 - 13. Two strings, each 15.0 m long, are stretched...Ch. 11 - Prob. 14PCh. 11 - Prob. 15PCh. 11 - Prob. 16PCh. 11 - Prob. 17PCh. 11 - 18. The speed of sound in air at room temperature...Ch. 11 - Prob. 19PCh. 11 - Prob. 20PCh. 11 - 21. A fisherman notices a buoy bobbing up and down...Ch. 11 - Prob. 22PCh. 11 - Prob. 23PCh. 11 - Prob. 24PCh. 11 - Prob. 25PCh. 11 - Prob. 26PCh. 11 - Prob. 27PCh. 11 - Prob. 28PCh. 11 - Prob. 29PCh. 11 - Problems 30–32. The graphs show displacement y as...Ch. 11 - Prob. 31PCh. 11 - 32. Rank the waves in order of maximum transverse...Ch. 11 - Prob. 33PCh. 11 - Prob. 34PCh. 11 - Prob. 35PCh. 11 - Prob. 36PCh. 11 - Prob. 37PCh. 11 - Prob. 38PCh. 11 - Prob. 39PCh. 11 - Prob. 40PCh. 11 - Prob. 41PCh. 11 - 42. A traveling sine wave is the result of the...Ch. 11 - Prob. 43PCh. 11 - Prob. 44PCh. 11 - Prob. 45PCh. 11 - Prob. 46PCh. 11 - Prob. 47PCh. 11 - Prob. 48PCh. 11 - Prob. 49PCh. 11 - Prob. 50PCh. 11 - Prob. 51PCh. 11 - Prob. 52PCh. 11 - Prob. 53PCh. 11 - Prob. 54PCh. 11 - Prob. 55PCh. 11 - Prob. 56PCh. 11 - Prob. 57PCh. 11 - Prob. 58PCh. 11 - Prob. 59PCh. 11 - Prob. 60PCh. 11 - Prob. 61PCh. 11 - Prob. 62PCh. 11 - Prob. 63PCh. 11 - Prob. 64PCh. 11 - Prob. 65PCh. 11 - Prob. 66PCh. 11 - Prob. 67PCh. 11 - Prob. 68PCh. 11 - Prob. 69PCh. 11 - Prob. 70PCh. 11 - Prob. 71PCh. 11 - Prob. 72PCh. 11 - Prob. 73PCh. 11 - Prob. 74PCh. 11 - Prob. 75PCh. 11 - Prob. 76PCh. 11 - Prob. 77PCh. 11 - Prob. 79PCh. 11 - Prob. 78PCh. 11 - Prob. 80PCh. 11 - Prob. 81PCh. 11 - Prob. 82PCh. 11 - Prob. 83PCh. 11 - Prob. 84PCh. 11 - Prob. 85PCh. 11 - Prob. 86PCh. 11 - Prob. 87PCh. 11 - Prob. 88PCh. 11 - Prob. 89PCh. 11 - Prob. 90PCh. 11 - Prob. 91PCh. 11 - Prob. 92PCh. 11 - Prob. 93PCh. 11 - Prob. 94PCh. 11 - Prob. 95PCh. 11 - Prob. 96PCh. 11 - Prob. 97PCh. 11 - Prob. 98PCh. 11 - Prob. 99PCh. 11 - Prob. 100PCh. 11 - Prob. 102PCh. 11 - 102. A harpsichord string is made of yellow brass...
Knowledge Booster
Background pattern image
Physics
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.
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Wave Speed on a String - Tension Force, Intensity, Power, Amplitude, Frequency - Inverse Square Law; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=vEzftaDL7fM;License: Standard YouTube License, CC-BY
Vibrations of Stretched String; Author: PhysicsPlus;https://www.youtube.com/watch?v=BgINQpfqJ04;License: Standard Youtube License