/*! 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} Q9E Which of the following wave func... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q9E (page 497)

Which of the following wave functions satisfies the wave equation, Eq. (15.12)? (a)\(y\left( {x,t} \right) = Acos\left( {kx + \omega t} \right)\) ; (b)\(y\left( {x,t} \right) = Asin\left( {kx + \omega t} \right)\) ; (c) \(y\left( {x,t} \right) = A\left( {coskx + cos\omega t} \right)\) (d) For the wave of part (b), write the equations for the transverse velocity and transverse acceleration of a particle at point x.

Short Answer

Expert verified

(a) Wave equation Eq. (15.12) is satisfied, if \(\nu = \frac{\omega }{k}\)

Step by step solution

01

Given data

\(y\left( {x,t} \right) = Acos\left( {kx + \omega t} \right)\)

02

Concept/ Formula used

Wave equation involves second partial derivatives of wave function.

\(\frac{{{\partial ^2}y\left( {x,t} \right)}}{{\partial {x^2}}} = \frac{1}{{{\nu ^2}}}\frac{{{\partial ^2}y\left( {x,t} \right)}}{{\partial {t^2}}}\) . . . (15.12)

Where,\(\nu \)is wave speed.

03

Verification for wave function

(a)

\(\begin{aligned}{l}\frac{{{\partial ^2}y\left( {x,t} \right)}}{{\partial {x^2}}} = - A{k^2}\cos \left( {kx + \omega t} \right)\\\frac{{{\partial ^2}y\left( {x,t} \right)}}{{\partial {t^2}}} = - A{\omega ^2}\cos \left( {kx + \omega t} \right)\\\end{aligned}\)\(\)

Wave equation Eq. (15.12) is satisfied, if \(\nu = \frac{\omega }{k}\)

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

A long rope with mass m is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope, and the pulse travels up the rope. Does the speed of the wave pulse change as it moves up the rope, and if so, does it increase or decrease? Explain.

In case 1, a source of sound approaches a stationary observer at speed u. In case 2, the observer moves toward the stationary source at the same speed u. If the source is always producing the same frequency sound, will the observer hear the same frequency in both cases, since the relative speed is the same each time? Why or why not?

Two swift canaries fly toward each other, each moving at 15.0 m/s relative to the ground, each warbling a note of frequency 1750 Hz. (a) What frequency note does each bird hear from the other one? (b) What wavelength will each canary measure for the note from the other one?

BIO Human Hearing. A fan at a rock concert is 30 m from the stage, and at this point the sound intensity level is 110 dB (a) How much energy is transferred to her eardrums each second? (b) How fast would a 2.0-mg mosquito have to fly (in mm/s) to have this much kinetic energy? Compare the mosquito鈥檚 speed with that found for the whisper in part (a) of Exercise 16.13.

Two identical loudspeakers are located at points A and B, 2.00 m apart. The loudspeakers are driven by the same amplifier and produce sound waves with a frequency of 784 Hz. Take the speed of sound in air to be 344 m/s. A small microphone is moved out from point Balong a line perpendicular to the line connecting Aand B(line BC in Fig. P16.65). (a) At what distances from Bwill there be destructiveinterference? (b) At what distances from Bwill there be constructiveinterference? (c) If the frequency is made low enough, there will be no positions along the line BCat which destructive interference occurs. How low must the frequency be for this to be the case?
See all solutions

Recommended explanations on Physics Textbooks

Famous Physicists

Read Explanation

Radiation

Read Explanation

Mechanics and Materials

Read Explanation

Translational Dynamics

Read Explanation

Rotational Dynamics

Read Explanation

Oscillations

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.