Question

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is $$y_{R}(x, t)=0.70 \mathrm{m} \sin \left(3.00 \mathrm{m}^{-1} x-6.28 \mathrm{s}^{-1} t+\pi / 16 \mathrm{rad}\right)$$,What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?

Name: Problem 97, Chapter 16: University Physics Volume 1
Uploaded: 2020-07-04T23:25:55-08:00
Duration: 1 min 19 s
Channel: Mayukh Banik
Description: Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is yR(x, t)=0.70 m sin(3.00 m^-1 x-6.28 s^-1 t+π/ 16 rad),What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?

   Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is $$y_{R}(x, t)=0.70 \mathrm{m} \sin \left(3.00 \mathrm{m}^{-1} x-6.28 \mathrm{s}^{-1} t+\pi / 16 \mathrm{rad}\right)$$,What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?

University Physics Volume 1

Samuel J. Ling, Jeff… 1st Edition

Chapter 16, Problem 97

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Solved by Expert Mayukh Banik

07/04/2020

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70 \mathrm{m} \sin \left(3.00 \mathrm{m}^{-1} x-6.28 \mathrm{s}^{-1} t+\pi / 16 \mathrm{rad}\right)$$ Show more…

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Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is $$y_{R}(x, t)=0.70 \mathrm{m} \sin \left(3.00 \mathrm{m}^{-1} x-6.28 \mathrm{s}^{-1} t+\pi / 16 \mathrm{rad}\right)$$,What are the angular frequency, wave number, amplitude, and phase shift of the individual waves?

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Key Concepts

Angular Frequency

Angular frequency is a measure of how quickly the wave oscillates in time, expressed in radians per second. It appears as the coefficient of the time variable in the sinusoidal function and determines the temporal periodicity of the wave.

Wave Number

Wave number describes the spatial frequency of the wave; it is the number of radians per unit distance. It appears as the coefficient of the spatial variable and determines how rapidly the phase changes with position.

Amplitude

Amplitude is the maximum displacement of the wave from its equilibrium position. It indicates the strength or energy of the wave and is given by the coefficient outside the sine function.

Phase Shift

Phase shift represents the horizontal translation of the wave function. It indicates the shift in the starting point of the sine wave’s cycle and is added to the phase in the argument of the sine function.

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