What physical quantity is the same for $X$-rays of wavelength $10^{-10} \; m$,red light of wavelength $6800 \; \mathring{A}$,and radio waves of wavelength $500 \; m$?

The speed of an electromagnetic wave in a vacuum depends upon the source of radiation.

If a source is transmitting electromagnetic waves of frequency $8.196 \times 10^{6} \ Hz$,then the wavelength of the $EM$ waves transmitted from the source will be . . . . . . . (in $cm$)

Out of the following options,which one can be used to produce a propagating electromagnetic wave?

The electric field of an electromagnetic wave in free space is given by $\vec E = 10 \cos (10^7 t + kx) \hat j \, V/m$,where $t$ and $x$ are in seconds and metres respectively. It can be inferred that:
$(1)$ The wavelength $\lambda$ is $188.4 \, m$.
$(2)$ The wave number $k$ is $0.33 \, rad/m$.
$(3)$ The wave amplitude is $10 \, V/m$.
$(4)$ The wave is propagating along $+x$ direction.
Which one of the following pairs of statements is correct?

An electromagnetic wave is represented by the electric field $\vec{E} = E_0 \hat{n} \sin [\omega t + (6y - 8z)]$. Taking unit vectors in $x, y$ and $z$ directions to be $\hat{i}, \hat{j}$ and $\hat{k}$,the direction of propagation $\hat{s}$ is: