9) A sinusoidal wave of frequency 500 Hz has a velocity of 350 m/sec. a) How far apart are (2) points that differ in phase by t/3 radians? b) What is the wavelength of the wave? c) What is the time interval between these (2) points? d) What is the period of the wave? e) What is the angular frequency? f) What is the constant of propagation?

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)...
icon
Related questions
Question
**Question 9: Analysis of a Sinusoidal Wave**

Consider a sinusoidal wave with a frequency of 500 Hz and a velocity of 350 m/s.

a) How far apart are two points that differ in phase by \(\pi/3\) radians?

b) What is the wavelength of the wave?

c) What is the time interval between these two points?

d) What is the period of the wave?

e) What is the angular frequency?

f) What is the constant of propagation?

**Detailed Explanation:**

- **Wavelength and Phase Difference:** 
  To find how far apart two points are that differ in phase by \(\pi/3\) radians, use the relationship between wavelength \(\lambda\), wave number \(k\), and phase difference.

- **Wavelength (\(\lambda\)):** 
  It is given by \(\lambda = \frac{v}{f}\), where \(v\) is the velocity and \(f\) is the frequency.

- **Time Interval:**
  The time interval between these points can be determined through the relation of phase difference to time.

- **Period (\(T\)):**
  The period of the wave is the reciprocal of the frequency.

- **Angular Frequency (\(\omega\)):**
  Angular frequency is calculated by \(\omega = 2\pi f\).

- **Constant of Propagation (Wave Number \(k\)):**
  It is determined by \(k = \frac{2\pi}{\lambda}\).

These concepts are crucial for understanding wave properties and behaviors in physics.
Transcribed Image Text:**Question 9: Analysis of a Sinusoidal Wave** Consider a sinusoidal wave with a frequency of 500 Hz and a velocity of 350 m/s. a) How far apart are two points that differ in phase by \(\pi/3\) radians? b) What is the wavelength of the wave? c) What is the time interval between these two points? d) What is the period of the wave? e) What is the angular frequency? f) What is the constant of propagation? **Detailed Explanation:** - **Wavelength and Phase Difference:** To find how far apart two points are that differ in phase by \(\pi/3\) radians, use the relationship between wavelength \(\lambda\), wave number \(k\), and phase difference. - **Wavelength (\(\lambda\)):** It is given by \(\lambda = \frac{v}{f}\), where \(v\) is the velocity and \(f\) is the frequency. - **Time Interval:** The time interval between these points can be determined through the relation of phase difference to time. - **Period (\(T\)):** The period of the wave is the reciprocal of the frequency. - **Angular Frequency (\(\omega\)):** Angular frequency is calculated by \(\omega = 2\pi f\). - **Constant of Propagation (Wave Number \(k\)):** It is determined by \(k = \frac{2\pi}{\lambda}\). These concepts are crucial for understanding wave properties and behaviors in physics.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 6 steps

Blurred answer
Knowledge Booster
Stretched string
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
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
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…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON