The magnetic field in a plane monochromatic electromagnetic wave with wavelength λ = 598 nm, propagating in a vacuum in the z-direction is described by b =(b1sin(kz−ω+j^) where b1 = 8.7 x 10-6 t, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively. what is k, the wavenumber of this wave?

For this given plane monochromatic electromagnetic wave with wavelength λ=598 nm, the wavenumber is .

Explanation:

For a plane electromagnetic wave we have that the electrical and magnetic field are:

In this case we have the data for the magnetic field. We are told that the magnetic field in a plane electromagnetic wave with wavelength λ=598 nm, propagating in a vacuum in the z direction () is described by

( are the unit vectors in the x,y,z directions respectively)

The wavenumber k is a measure of the spatial frequency of the wave, is defined as the number of radians per unit distance:

where λ is the wavelength

So we get that

The wavenumber is

            .

a longitudinal wave moves energy that is to the direction of the wave’s movement. - true

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2