1 Mechanical Wave A string is set up as shown. One end of the string is attached to an oscillator (which oscillates up and down). The rest of the string is strung over a frictionless pulley, and a weight with mass m - 4 kg hangs from the other end. From the oscillator to the pulley, the length of the string is L=2.0 m. In this setup, the pulley acts as a fixed end for wave reflections. oscillator m (a) The oscillator is driving the string's motion with frequency f₁ = 25 Hz, the lowest frequency to create a standing wave in the string. What is the wave's speed? (b) What is the magnitude of the tension in the string? (c) If the full length of the string (L+ distance hanging over the pulley) is 2.5 m, what is the mass of the string? (d) Now assume that the oscillator sends a single wave pulse with height 4 cm, which can be described by the general equation of motion, y(r, t) = Asin(kr-wt). What is the specific equation of motion for this scenario? [Hint: What are your values for A, k, w? What are the expressions for the speed and acceleration of particles on the string? (f) What are the maximum speed and acceleration for a particle on the string?
1 Mechanical Wave A string is set up as shown. One end of the string is attached to an oscillator (which oscillates up and down). The rest of the string is strung over a frictionless pulley, and a weight with mass m - 4 kg hangs from the other end. From the oscillator to the pulley, the length of the string is L=2.0 m. In this setup, the pulley acts as a fixed end for wave reflections. oscillator m (a) The oscillator is driving the string's motion with frequency f₁ = 25 Hz, the lowest frequency to create a standing wave in the string. What is the wave's speed? (b) What is the magnitude of the tension in the string? (c) If the full length of the string (L+ distance hanging over the pulley) is 2.5 m, what is the mass of the string? (d) Now assume that the oscillator sends a single wave pulse with height 4 cm, which can be described by the general equation of motion, y(r, t) = Asin(kr-wt). What is the specific equation of motion for this scenario? [Hint: What are your values for A, k, w? What are the expressions for the speed and acceleration of particles on the string? (f) What are the maximum speed and acceleration for a particle on the string?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Topic Video
Question
Please solve the following
![# Mechanical Wave
A string is set up as shown. One end of the string is attached to an oscillator (which oscillates up and down). The rest of the string is strung over a frictionless pulley, and a weight with mass \( m = 4 \, \text{kg} \) hangs from the other end. From the oscillator to the pulley, the length of the string is \( L = 2.0 \, \text{m} \). In this setup, the pulley acts as a fixed end for wave reflections.
### Diagram Description
- **Oscillator**: Positioned at the left end of the string.
- **String**: Extends horizontally from the oscillator, passing over a frictionless pulley.
- **Pulley**: Located to the right, supporting the string.
- **Mass**: A \( 4 \, \text{kg} \) weight hangs vertically from the string after it passes over the pulley.
### Questions
(a) **Wave Speed**: The oscillator drives the string’s motion with frequency \( f_1 = 25 \, \text{Hz} \), the lowest frequency to create a standing wave in the string. What is the wave’s speed?
(b) **Tension in the String**: What is the magnitude of the tension in the string?
(c) **Mass of the String**: If the full length of the string (L plus the distance hanging over the pulley) is \( 2.5 \, \text{m} \), what is the mass of the string?
(d) **Equation of Motion**: Assume the oscillator sends a wave pulse with height \( 4 \, \text{cm} \), described by \( y(x, t) = A \sin(kx - \omega t) \). What is the specific equation of motion for this scenario? [Hint: Determine the values for \( A, k, \omega \)]
(e) **Speed and Acceleration Expressions**: What are the expressions for the speed and acceleration of particles on the string?
(f) **Maximum Speed and Acceleration**: What are the maximum speed and acceleration for a particle on the string?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0a663478-8026-4bb7-815e-65d37446f03b%2Fa51668d9-eaa5-456f-beb5-588315e45fee%2Fpxmry7t_processed.png&w=3840&q=75)
Transcribed Image Text:# Mechanical Wave
A string is set up as shown. One end of the string is attached to an oscillator (which oscillates up and down). The rest of the string is strung over a frictionless pulley, and a weight with mass \( m = 4 \, \text{kg} \) hangs from the other end. From the oscillator to the pulley, the length of the string is \( L = 2.0 \, \text{m} \). In this setup, the pulley acts as a fixed end for wave reflections.
### Diagram Description
- **Oscillator**: Positioned at the left end of the string.
- **String**: Extends horizontally from the oscillator, passing over a frictionless pulley.
- **Pulley**: Located to the right, supporting the string.
- **Mass**: A \( 4 \, \text{kg} \) weight hangs vertically from the string after it passes over the pulley.
### Questions
(a) **Wave Speed**: The oscillator drives the string’s motion with frequency \( f_1 = 25 \, \text{Hz} \), the lowest frequency to create a standing wave in the string. What is the wave’s speed?
(b) **Tension in the String**: What is the magnitude of the tension in the string?
(c) **Mass of the String**: If the full length of the string (L plus the distance hanging over the pulley) is \( 2.5 \, \text{m} \), what is the mass of the string?
(d) **Equation of Motion**: Assume the oscillator sends a wave pulse with height \( 4 \, \text{cm} \), described by \( y(x, t) = A \sin(kx - \omega t) \). What is the specific equation of motion for this scenario? [Hint: Determine the values for \( A, k, \omega \)]
(e) **Speed and Acceleration Expressions**: What are the expressions for the speed and acceleration of particles on the string?
(f) **Maximum Speed and Acceleration**: What are the maximum speed and acceleration for a particle on the string?
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 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY