Answer to Question #180802 in Optics for Khushi

Question #180802

a) The mathematical expression for one dimensional wave travelling along the

positive x-direction is given as

y(x,t )  0.02 sin (42 x 1886t )m

where x is in meters and t is in seconds. Determine the direction of propagation of

the wave and calculate its amplitude, wavelength, frequency and velocity.


1
Expert's answer
2021-04-14T11:34:18-0400

Given,

"y(x,t)=0.02\\ sin(42x- 1886t)"


1.) Amplitude:

The amplitude is whatever is multiplying the sine.

Amplitude A = 0.02 units


2.) Wavelength:

The wavenumber k is whatever is multiplying the x:

k = 42 m-1

So, wavelength "\\lambda =\\dfrac{2\\pi}{k}=0.15\\ m"


3.) Frequency:

The angular frequency w is whatever is multiplying the t.

"\\omega" = 1886 rad/s

So, frequency "f=\\dfrac{\\omega}{2\\pi}=\\dfrac{1886}{2\\pi}=300.16\\ Hz"


4.) Velocity:

The wave velocity can be found from the frequency and wavelength:

"v=f\\lambda=300.16\\times 0.15=45.02\\ \\ m\/s"


And, to find the direction of propagation of the wave, just look at the sign between the x and t terms in the equation. In our case we have a minus sign:

So, A negative sign means the wave is traveling in the +x direction.



Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS