A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, an element of the string at x = 0 has %3D %3D a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s. (a) What is the amplitude of the wave? (b) What is the initial phase angle? (c) What is the maximum transverse speed of an element of the string?
A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, an element of the string at x = 0 has %3D %3D a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s. (a) What is the amplitude of the wave? (b) What is the initial phase angle? (c) What is the maximum transverse speed of an element of the string?
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Question
100%
I am confused on how to start this problem. I know I need to use the y(x,t)=Asin(kx+wt+phi) formula, but do I need to take the derivative of that once I enter in all the variables? I am referenceing the problem 14 in the pic I attached. Thanks!
![**Chapter 12**
A transverse sinusoidal wave on a string has a period \( T = 25 \) ms and travels in the negative \( x \) direction with a speed of 30 m/s. At \( t = 0 \), an element of the string at \( x = 0 \) has a transverse position of 2 cm and is traveling downward with a speed of 2 m/s.
A) What is the amplitude of the wave?
B) What is the initial phase angle?
C) What is the maximum transverse speed of an element of the string?
D) Write the wave function for the wave.
- **Given:**
- \( T = 25 \) ms = 0.025 s
- \( v = 30 \) m/s
- **At \( t = 0 \):**
- \( x = 0 \)
- \( y = 0.02 \) m
- **Wave number \( k = \frac{2\pi}{\lambda} \):**
\[
\omega = 2\pi f = 251.33 \, \text{rad/s}
\]
\[
v_y = 2 \, \text{m/s}
\]
- **Maximum transverse speed formula:**
\[
v_{y \text{max}} = \omega A
\]
- **Frequency calculation:**
\[
f = \frac{1}{T} = 40 \, \text{Hz}
\]
- **Wave Function:**
- As per page 420 (since \( x = 0 \) and \( t = 0 \)), use:
\[
y(x, t) = A \sin(kx - \omega t + \phi)
\]
**Diagram Explanation:**
The diagram features a sinusoidal wave graph labeled with essential notations:
1. The wave appears as a typical sinusoid illustrating one full wavelength (\( \lambda \)).
2. Key elements labeled:
- Amplitude (\( A \))
- Wavelength (\( \lambda \))
- Displacement along the \( x \) and \( y \) axes, showing the motion in both positive and negative directions.
3. The graph provides a visual representation of the wave equation parameters, helping to contextualize wave movement and position with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8854ffd-431b-44a2-b47e-daec534c3a26%2Fcf94d964-4a63-49fb-bc0c-cc33146e295e%2Fti8hzo.jpeg&w=3840&q=75)
Transcribed Image Text:**Chapter 12**
A transverse sinusoidal wave on a string has a period \( T = 25 \) ms and travels in the negative \( x \) direction with a speed of 30 m/s. At \( t = 0 \), an element of the string at \( x = 0 \) has a transverse position of 2 cm and is traveling downward with a speed of 2 m/s.
A) What is the amplitude of the wave?
B) What is the initial phase angle?
C) What is the maximum transverse speed of an element of the string?
D) Write the wave function for the wave.
- **Given:**
- \( T = 25 \) ms = 0.025 s
- \( v = 30 \) m/s
- **At \( t = 0 \):**
- \( x = 0 \)
- \( y = 0.02 \) m
- **Wave number \( k = \frac{2\pi}{\lambda} \):**
\[
\omega = 2\pi f = 251.33 \, \text{rad/s}
\]
\[
v_y = 2 \, \text{m/s}
\]
- **Maximum transverse speed formula:**
\[
v_{y \text{max}} = \omega A
\]
- **Frequency calculation:**
\[
f = \frac{1}{T} = 40 \, \text{Hz}
\]
- **Wave Function:**
- As per page 420 (since \( x = 0 \) and \( t = 0 \)), use:
\[
y(x, t) = A \sin(kx - \omega t + \phi)
\]
**Diagram Explanation:**
The diagram features a sinusoidal wave graph labeled with essential notations:
1. The wave appears as a typical sinusoid illustrating one full wavelength (\( \lambda \)).
2. Key elements labeled:
- Amplitude (\( A \))
- Wavelength (\( \lambda \))
- Displacement along the \( x \) and \( y \) axes, showing the motion in both positive and negative directions.
3. The graph provides a visual representation of the wave equation parameters, helping to contextualize wave movement and position with
Transcribed Image Text:Certainly! Here is the transcription suitable for an educational website:
---
### Problems on Wave Motion
**12.** GP A sinusoidal wave traveling in the negative x direction (to the left) has an amplitude of 20.0 cm, a wavelength of 35.0 cm, and a frequency of 12.0 Hz. The transverse position of an element of the medium at t = 0, x = 0 is y = –3.00 cm, and the element has a positive velocity here. We wish to find an expression for the wave function describing this wave.
(a) Sketch the wave at t = 0.
(b) Find the angular wave number k from the wavelength.
(c) Find the period T from the frequency.
(d) Find the angular frequency ω.
(e) Find the wave speed v.
(f) From the information about t = 0, find the phase constant φ.
(g) Write an expression for the wave function y(x, t).
**13.** W When a particular wire is vibrating with a frequency of 4.00 Hz, a transverse wave of wavelength 60.0 cm is produced. Determine the speed of waves along the wire.
**14.** A transverse sinusoidal wave on a string has a period T = 25.0 ms and travels in the negative x direction with a speed of 30.0 m/s. At t = 0, an element of the string at x = 0 has a transverse position of 2.00 cm and is traveling downward with a speed of 2.00 m/s.
(a) What is the amplitude of the wave?
(b) What is the initial phase angle?
(c) What is the maximum transverse speed of an element of the string?
(d) Write the wave function for the wave.
### Section 13.3 The Speed of Transverse Waves on Strings
**15.** M A steel wire of length 30.0 m and a copper wire of length 20.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 150 N. During what time interval will a transverse wave travel the entire length of the two wires?
---
This text provides a series of problems related to wave functions and properties, specifically focusing on sinusoidal waves in different scenarios, including traveling waves and waves on wires. Diagrams or graphs are not included
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON