**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.

∆x=λ2π∆ϕ=v2πf∆ϕ=350 m/s2π500 Hzπ3=0.117 m

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?

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)...

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A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

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