Answer to Question #180802 in Optics for Khushi

Question

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.

Answer 1

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.