Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 16, Problem 15P

(a)

To determine

The transverse speed of the wave.

(a)

Expert Solution
Check Mark

Answer to Problem 15P

The transverse speed of the wave is 1.51m/s_.

Explanation of Solution

Write the general expression for wave function of a wave moving in positive x direction.

  y=Asin(kxωt+ϕ)                                                                                                (I)

Here, A is the amplitude of the wave, k is the wave number, ω is the angular frequency, and ϕ is the phase.

The wave function of the given wave.

  y=(0.120)sin(π8x+4πt)                                                                             (II)

The transverse speed will be obtained by taking the derivative of the position of the wave.

The expression for maximum speed is.

  υy=yt                                                                                                         (III)

Conclusion:

Substitute, (0.120)sin(π8x+4πt)0.100sin(πxπt) for y in equation (III).

  υy=((0.120)sin(π8x+4πt))t=0.120(4π)cos(π8x+4πt)                                                                      (IV)

Substitute, 0.200s for t, and 1.60m for x in equation (IV).

  υy=0.120(4π)cos(π8(1.60m)+4π(0.200s))=1.51m/s

Therefore, the transverse speed of any element on the string is 1.51m/s_.

(b)

To determine

The transverse acceleration at t=0.200s, and x=1.60m.

(b)

Expert Solution
Check Mark

Answer to Problem 15P

The transverse acceleration at t=0.200s, and x=1.60m is 0_.

Explanation of Solution

Transverse acceleration will be obtained by taking the derivative of transverse velocity with respect to time.

Write the expression for transverse acceleration.

  ay=υyt                                                                                                        (V)

Conclusion:

Substitute, 0.120(4π)cos(π8x+4πt) for υy in equation (V).

  ay=(0.120(4π)cos(π8x+4πt))t=0.120(4π)2sin(π8x+4πt)                                                                      (VI)

Substitute, 0.200s for t, and 1.60m for x in equation (VI).

  ay=0.120(4π)2sin(π8(1.60m)+4π(0.200s))=0

Therefore, the transverse acceleration at t=0.200s, and x=1.60m is 0_.

(c)

To determine

The wavelength of the wave.

(c)

Expert Solution
Check Mark

Answer to Problem 15P

The wavelength of the wave is 1.60m_.

Explanation of Solution

Write the expression for wavelength of the wave in terms of wave number.

  λ=2πk                                                                                                       (VII)

Here, k is the wave number.

Comparing equation (I) and (II), the wave number is π8.

Conclusion:

Substitute, π8 for k in equation (V).

  λ=2π(π8)=1.60m

Therefore, the wavelength of the wave is 1.60m_.

(d)

To determine

The period of the wave.

(d)

Expert Solution
Check Mark

Answer to Problem 15P

The period of the wave is 0.500s_.

Explanation of Solution

Write the expression for the period of the wave.

  T=2πω                                                                                                      (VIII)

Here, ω is the angular frequency

Comparing equation (I) and (II), the angular frequency is 4π.

Conclusion:

Substitute, 4π for ω in equation (VI)

  T=2π4π=0.500s

Therefore, the period of the wave is 0.500s_.

(e)

To determine

The speed of an element of propagation of wave.

(e)

Expert Solution
Check Mark

Answer to Problem 15P

The speed of an element of propagation of wave is 32.0m/s_.

Explanation of Solution

Write the expression for speed.

  υ=fλ=λT (IX)

Conclusion:

Substitute, 1.60m for λ , and 0.500s for T in equation (IX).

  υ=1.60m0.500s=32.0m/s

Therefore, the speed of an element of propagation of wave is 32.0m/s_.

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!
Students have asked these similar questions
Please solve
A piece of silicon semiconductor has length L=0.01cm and cross-section in a square shape with an area of A=5×10−4cm2 . The semiconductor is doped with 1012cm−3 Phosphorus atoms and 1017cm−3 Boron atoms. An external electric field E=1.5×104N/C is applied to the silicon piece along the length direction, through the cross section. What is the total current in the silicon at T=300K? Assume the mobility of silicon is 1400cm2V−1s−1 for electrons and 450cm2V−1s−1 for holes, respectively. Assume the intrinsic carrier concentration in silicon is 1010cm−3 . Give your answer in mA, rounded to 3 significant figures. Just enter the number, nothing else.
An impurity with a charge of 2e is placed in a three-dimensional metal. Assume that the Friedel sum rule holds for this system, and only the scattering phase shifts from the electrons contribute to this sum (we don't need to consider ion phase shifts). This metal has a spherical Fermi surface with Fermi wave vector kF . The only degeneracy for the electrons at the Fermi surface is spin (two-fold) and angular momentum ( 2l+1 for each angular momentum l ). Ignore scattering for l>2 and assume that the scattering doesn't depend on the spin degree of freedom. Denote the scattering phase shift at the Fermi wave vector in the l -th angular momentum channel as δl(kF) . If δ0(kF)=11π31 , and δ1(kF)=π29 , what is δ2(kF)? Round your answer to three significant figures. Just enter the number, nothing else.

Chapter 16 Solutions

Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University

Ch. 16 - Prob. 6OQCh. 16 - Prob. 7OQCh. 16 - Prob. 8OQCh. 16 - Prob. 9OQCh. 16 - Prob. 1CQCh. 16 - Prob. 2CQCh. 16 - Prob. 3CQCh. 16 - Prob. 4CQCh. 16 - Prob. 5CQCh. 16 - Prob. 6CQCh. 16 - Prob. 7CQCh. 16 - Prob. 8CQCh. 16 - Prob. 9CQCh. 16 - A seismographic station receives S and P waves...Ch. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Two points A and B on the surface of the Earth are...Ch. 16 - Prob. 5PCh. 16 - Prob. 6PCh. 16 - Prob. 7PCh. 16 - Prob. 8PCh. 16 - Prob. 9PCh. 16 - When a particular wire is vibrating with a...Ch. 16 - Prob. 11PCh. 16 - Prob. 12PCh. 16 - Prob. 13PCh. 16 - Prob. 14PCh. 16 - Prob. 15PCh. 16 - Prob. 16PCh. 16 - Prob. 17PCh. 16 - A sinusoidal wave traveling in the negative x...Ch. 16 - Prob. 19PCh. 16 - Prob. 20PCh. 16 - Prob. 21PCh. 16 - Prob. 22PCh. 16 - Prob. 23PCh. 16 - Prob. 24PCh. 16 - An Ethernet cable is 4.00 m long. The cable has a...Ch. 16 - Prob. 26PCh. 16 - Prob. 27PCh. 16 - Prob. 28PCh. 16 - Tension is maintained in a string as in Figure...Ch. 16 - Prob. 30PCh. 16 - Prob. 31PCh. 16 - Prob. 32PCh. 16 - Transverse waves are being generated on a rope...Ch. 16 - Prob. 34PCh. 16 - Prob. 35PCh. 16 - Prob. 36PCh. 16 - Prob. 37PCh. 16 - A horizontal string can transmit a maximum power...Ch. 16 - Prob. 39PCh. 16 - A two-dimensional water wave spreads in circular...Ch. 16 - Prob. 41PCh. 16 - Prob. 42PCh. 16 - Show that the wave function y = eb(x vt) is a...Ch. 16 - Prob. 44PCh. 16 - Prob. 45APCh. 16 - Prob. 46APCh. 16 - Prob. 47APCh. 16 - Prob. 48APCh. 16 - Prob. 49APCh. 16 - Prob. 50APCh. 16 - A transverse wave on a string is described by the...Ch. 16 - A sinusoidal wave in a string is described by the...Ch. 16 - Prob. 53APCh. 16 - Prob. 54APCh. 16 - Prob. 55APCh. 16 - Prob. 56APCh. 16 - Prob. 57APCh. 16 - Prob. 58APCh. 16 - A wire of density is tapered so that its...Ch. 16 - Prob. 60APCh. 16 - Prob. 61APCh. 16 - Prob. 62APCh. 16 - Prob. 63APCh. 16 - Prob. 64CPCh. 16 - Prob. 65CPCh. 16 - Prob. 66CPCh. 16 - Prob. 67CP
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.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
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