Log out Go to App
Go to App

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

One end of a horizontal rope is attached to a prong of another end passes over a pulley and supports a 1.50-kg mass. The linear mass density of the rope is 0.0480 kg/m. (a) What is the speed of a transverse wave on the rope? (b) What is the wavelength? (c) How would you answer to parts (a) and (b) change if the mass were increased to 3.00 kg?

A 75.0-cm-long wire of mass 5.625 g is tied at both ends and adjusted to a tension of 35.0 N. When it is vibrating in its second overtone, find (a) the frequency and wavelength at which it is vibrating and (b) the frequency and wavelength of the sound waves it is producing.

Lane dividers on highways sometimes have regularly

spaced ridges or ripples. When the tires of a moving car roll along

such a divider, a musical note is produced. Why? Explain how this

phenomenon could be used to measure the car’s speed.

Does an aircraft make a sonic boom only at the instant its speed exceeds Mach 1? Explain.

In most modern wind instruments the pitch is changed by

using keys or valves to change the length of the vibrating air column.

The bugle, however, has no valves or keys, yet it can play many notes. How might this be possible? Are there restrictions on what notes a bugle can play?
See all solutions

Recommended explanations on Physics Textbooks

Quantum Physics

Read Explanation

Fluids

Read Explanation

Fundamentals of Physics

Read Explanation

Mechanics and Materials

Read Explanation

Space Physics

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.

Sign-up for free