Question

A plane electromagnetic wave, with wavelength 2.8 m, travels in vacuum in the positive direction of an x axis. the electric field, of amplitude 260 v/m, oscillates parallel to the y axis. what are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave

Answer 1

Ok first you gotta know what they are actually even asking you.

Frequency = wavelengths per second
Angular Frequency = radians per second
Wave Number = wavelengths per meter
Angular Wave Number = radians per meter

Frequency is Easy, just divide the speed of light by the wavelength. This is your answer for A.

Angular frequency is how many radians per second the ELECTRIC FIELD moves through over one second. We know that there are 2π radians in one wavelength.

So to get the angular frequency just multiply the regular frequency by 2π (6.28) to get the frequency in terms of radians per second (instead of waves per second). This is your answer for B.

The wave number of a photon is how many waves per meter the photon moves through rather than waves per second, similar but different to the 'frequency' calculations above.

Simply find the waves per meter (1 meter divided by the wavelength) and multiply by 2π to get the radians per meter. this is your answer for C.

NOTE: make sure your units are all correct, wavelength in meters, frequency in Hz etc...