The Mathematical Description of a Wave Video Lessons

Concept

Problem: A traveling wave along the x-axis is given by the following wave function y(x,t) = 3.9 cos(2.8x - 9.2t + 0.58) With x in meters, t in seconds, and y in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this wave. 1. What is the amplitude, in meters? 2. What is the frequency, in Hz? 3. What is the wavelength, in meters? 4. What is the wave speed, in meters per second? 5. What is the phase constant, in radians? A. 3.9B. 2.8C. 2.8/2πD. 2π/2.8E. 9.2F. 9.2/2πG. 2π/9.2H. 0.58I. 0.58•(180°/π)J. 0.58•(π/180°)K. 2.8•9.2L. 28/9.2M. 9.2/2.8N. Some other value

FREE Expert Solution

The general wave solution for a wave travelling in the x-axis is:

$\overline{){\mathbf{y}}{\mathbf{\left(}}{\mathbf{x}}{\mathbf{,}}{\mathbf{t}}{\mathbf{\right)}}{\mathbf{=}}{\mathbf{A}}{\mathbf{c}}{\mathbf{o}}{\mathbf{s}}{\mathbf{\left(}}{\mathbf{k}}{\mathbf{x}}{\mathbf{-}}{\mathbf{\omega }}{\mathbf{t}}{\mathbf{+}}{\mathbf{\varphi }}{\mathbf{\right)}}}$ A is the amplitude.

1.

Comparing the wave function to the general solution:

A = 3.9m

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Problem Details

A traveling wave along the x-axis is given by the following wave function

y(x,t) = 3.9 cos(2.8x - 9.2t + 0.58)

With x in meters, t in seconds, and y in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this wave.

1. What is the amplitude, in meters?

2. What is the frequency, in Hz?

3. What is the wavelength, in meters?

4. What is the wave speed, in meters per second?

5. What is the phase constant, in radians?

A. 3.9
B. 2.8
C. 2.8/2π
D. 2π/2.8
E. 9.2
F. 9.2/2π
G. 2π/9.2
H. 0.58
I. 0.58•(180°/π)
J. 0.58•(π/180°)
K. 2.8•9.2
L. 28/9.2
M. 9.2/2.8
N. Some other value